Soviet Foreign Minister Andrei Gromyko, an old hand at such things, called it "a necessary meeting" and the new boy on the block, Secretary of State Edmund S. Muskie, agreed.

Muskie picked up the phrase for public and private explanation of the intimate and important three-hour conference in Vienna Friday at which the senior diplomats of the two superpowers grappled for footing on the downward slope of Soviet-American relations.

In the wake of the meeting, the prospects are not good that Muskie and Gromyko will succeed in reversing the present dismal trend in a relationship that affects the tone and the substance of what many other nations do.

The way things are going, just about the best that can be expected is "a long, chilly plateau" in the relations of Washington and Moscow in the phrase of a well-informed American official.

At least as likely is that even the "chilly plateau" will prove illusory. In that case, this central political relationship of our times could drift downward, even downward into a new ice age of the cold war -- one that may last until the mid-1980s and possibly beyond.

This grim portrait of the present and future emerged from talks with American and Soviet officials, examination of recent events and attitudes, and also from traveling in the entourage of the new U.S. secretary of state last week as he sought to establish his authority within the U.S. government as well as internationally.

First, the good news -- about Muskie himself, who displayed an impressive capacity to operate and express himself effectively in a new field, "as surefooted as a cat" despite the new turf, according to a close observer.

Muskie showed a grasp of the issues and the politics of dealing with them that springs from a long career in senatorial and national politics as well as his absorptive and serious mind. More surprising, at age 66, he showed a zest and energy in the job. On the way home from Europe, he described the experience as "very exhilirating." This may reflect in part his recent boredom in the Senate.

Muskie also displayed bureaucratic prowess, though White House and State Department officials said it is untrue that David Aaron, deputy to presidential assistant Zbigniew Brzezinski, was shut out of the Gromyko meeting at the last minute. Aaron knew it was to be Muskie-Gromyko tete-a-tete when he left Washington for Vienna on other business last Thursday, officials said, but stood by with a gaggle of others in an anteroom of the talks in case of unexpected need.

Despite initial good marks from all sides, the coming of Muskie did not change the position of American diplomacy in any fundamental way. He brought a new face, but so far not a new policy or a new international situation. It would have been too much to expect, especially at this late stage of Carter's elected term, that Muskie could turn things around.

The most dramatic sign that Muskie is not magic was the sudden revelation that French President Valery Giscard d'Estaing is staging his own summit meeting in Poland with Soviet President Leonid Brezhnev, evidently to glorify his desired role of interlocutor between east and the rest of the west. Though there were whispers of such a plan in diplomatic corridors, according to American officials, Muskie was told nothing about it when he met French Foreign Minister Jean Francois-Poncet for 40 minutes in Vienna Friday morning.

Giscard's decision on this important matter was taken without advance consultations with Washington -- just the way American presidents in recent years took many such decisions without consulting the French or anyone else. Startled U.S. officials were publicly guarded but privately caustic about the French move yesterday.

For all their unhappiness with Giscard, it is hard for Washington officials to argue that he is interfering in the flow of a promising U.S. dialogue with the Soviets.

From informed accounts, what Muskie and Gromyko accomplished in their meeting in Vienna's Hofburg palace late Friday was to place most of their nations' complaints about one another face up on the table. But there was no conclusion about how to resolve them or even when or whether to talk about them again.

Both the substance and tone of the Muskie-Gromyko encounter seemed light years away from the summit meeting only last June in the same Hofburg Palace, where Carter and Brezhnev signed the strategic arms limitation treaty (SALT II) as a step, it was hoped, toward a new era of Soviet-American cooperation.

"God will not forgive us if we fail," said Brezhnev to Carter at their introduction there. Eleven months later, not only has the drive for amity collapsed, it has been supplanted by a new era of cross-purpose, confrontation and potential for eventual armed conflict.

American experts on the Soviet Union believe, moreover, that this is likely to be a relatively long and dangerous cycle of east-west antagonism rather than a setback of the moment. With military budgets soaring and attitudes hardening on both sides, the guesses about the duration of this time of troubles range from the couple of years to half a decade and beyond.

Both Soviet and American officials acknowledge that their relations were in trouble well before last June's sumit, though each side has its own view of the last-straw event that destroyed the basis for the former detente.

The United States emphasizes the Soviet invasion of Afghanistan last Dec. 27, the first use of Soviet ground troops outside the borders of the communist bloc since World War II and in U.S. eyes a threatening and unacceptable change in the rules of the international game.

Soviet emphasis, on the other hand, is placed on the decision by the United States and its NATO allies last Dec. 12 to deploy in Western Europe new and more powerful medium-range missiles, capable of striking Soviet territory. The Russians maintain this was a "betrayal" of the spirit, though not the letter, of the SALT drive to limit competition in nuclear arms.

These two sets of complaints reflect two basic and unresolved differences that have bedeviled Soviet-American relations for many years. One is a fundamental disagreement about whether the Soviet doctrine and practice of supporting and protecting revolutionary struggle in the Third World is compatible with U.S.-Soviet cooperation elsewhere. The other is the sharp conflict of views about relative military strength -- and relative vulnerability -- of the two superpowers and their allies.

In Vienna last June, Brezhnev stated explicitly to Carter that "solidarity with liberation struggles" is a principle of Soviet policy. Carter replied to Brezhnev, according to U.S. notes, that "we must restrict military intervention either directly or through third parties" in regional disputes. And in a foretaste of his commitment to the Persian Gulf, Carter added, "we must protect each nation's vital interest in access to crucial natural resources."

The marriage of Soviet logistics and Cuban troops in Angola beginning in 1975 and in the Ethiopian-Somali war starting in 1977 raised grave concern in Washington on this score. But the invasion of Afghanistan last December was even more serious because it was direct and unambiguous, and because the location of the country made it extremely sensitive both to Russia (as a border state) and to the west (because of proximity to Iran and the Persian Gulf).

In recent days Muskie has described the Soviet invasion as the cause of a "sea change" of U.S. perceptions about Moscow's intentions in the world. He continues to call on the Russians to withdraw from Afghanistan, and has come close to saying that such withdrawal will be necessary for ratification of the SALT II pact on nuclear arms and resumption of a broad U.S. cooperative relationship with Moscow.

There is no sign of Soviet intention or even consideration of withdrawal so long as the resistance within Afghanistan has not been crushed, and in the war zone itself the battle appears to be going poorly for the Russians. i

About the best that U.S. officials could hope, following Muskie's meeting with Gromyko, was that the Russians will now realize the full dimensions of American opposition to the Afghan action, and the nearly insurmountable barrier it poses to improvement of relations. Eventually, possible -- but not certainly or even probably -- this could bring a turnabout on the issue in Moscow.

The other cental issue in this classic quarrel is the divergent perception in east and west of relative military power. From the western view, the Soviets have reached military equality and are striving for superiority. In the Russian view, they are only recently military equals, and now the west is seeking to forge ahead toward renewed superiority.

In the Soviet calculation, the planned deployment of nearly 600 new, more powerful medium-range missiles in Western Europe, plus modernized French and British nuclear forces, will bring several thousand additional atomic warheads targeted on Soviet territory by the middle 1980s. These weapons are not covered by the "strategic arms" treaty signed in Vienna last June, but in the Soviet view there is little to choose between an in-coming nuclear weapon, whether it is based 500 miles or 10,000 miles away.

The Soviets see the European missiles as a "challenge" to new efforts on their part. The west sees them as a "response" to earlier Soviet improvements of their own medium-range missiles. In this cycle of attempted leapfrogging, the sides are never equal -- at least in the eyes of military planners -- and so there is no place to stop.

The same thing can happen in the field of strategic, long-range nuclear weapons, especially if the SALT agreement is permitted to collapse. This will be particularly dangerous because the demise of SALT will mean the end of the agreed-on rules against deliberate concealment, and thus an inevitable mushrooming of suspicion and fear, whether justified or unjustified. i

Deepening trouble and growing tensions between Washington and Moscow leave most of the rest of the world jittery and unhappy. The Eastern Europeans see their essential economic ties to the West in jeopardy, the Western Europeans see their military security and the internal political accommodations of left and right endangered, and the semi-neutrals such as Austria see the basis for their assured existence undermined. Because of the double standard, Washington is likely to be blamed more than Moscow.

The reduced margin for management in such circumstances is among the reasons that Muskie and most of his inherited State Department advisers believe Friday's meeting in Vienna, in Gromyko's word, was "necessary" -- even if it didn't settle anything.