President Carter's six-month balance sheet yesterday on strained relations with the Soviet Union was designed largely to assure Americans, some uneasy allies and highly suspicious Russians that there is no drift back toward "the cold war."

There was a notable understatement by the President on this underlying theme. He said: "We have made some progress toward our goals. But, to be frank, we also hear some negative comments from the Soviet side about SALT (nuclear strategic arms limitation talks) and about our more general relations."

By diplomatic measure, the "negative comments" have been a roar, not a whisper. There is a daily outpouring of caustic criticism from the Soviet Union that surpasses anything heard since "detente" was officially enshrined at the 1972 Moscow summit conference of Soviet leader Leonid I. Brezhnev and President Nixon.

This criticism has expanded from the original attacks on the Carter human rights and nuclear arms policies to wholesale chalenge in the Soviet press and radio broadcasts, Carter administration policy is now assailed as a return to "the methods of the cold war" in an attempt "to derail detente."

The basic Soviet charge, articulated by French President Valery Giscard 'd' Estaing in a Newsweek interview after his recent Paris meeting with Brezhnev, is: "Mr. Brezhnev feels that some of President Carter's decisions have broken what I will call the code of conduct of detente." The French president, impliedly sharing much of that view, said, "there is a profound misunderstanding between Washington and Moscow."

Administration officials made a point yesterday of emphasizing that Carter's Charleston, S.C., speech has been under discussion for about 10 days, long before the Giscard interview appeared. But that time frame only brings the sequence closer to the gloomy report given to Secretary State Cyrus R. Vance in Paris on June 24 about the Brezhnev-Giscard talks.

Before, and especially since, that meeting, top administration officials have said they were troubled by what president Carter openly expressed yesterday: are Soviet criticisms of his administration policy "based on a misconception of our motives," or are they "designed as propaganda to put pressure on us . . .?

Some administration strategists think the answer is yes on both counts. They believe the Soviet leadership is genuinely suspicious of the Carter policy which it regards as an overall challenge to the Kremlin's vital interests. Additionally, many U.S. planners believe that the Soviet Union is trying to reach over carter's head to the American public and to uneasy allies, to put counterpressure on the White House by raising the alaem of a return to cold war confrontation.

The President, in recent private talks with Democratic elder statesman Averell Harriman, with Marshall D. Shulman, another champion of U.S. Soviet detente and now chief Soviet adviser to Secretary Vance, sought to counter Soviet attempts to build a backfire against him inside the socalled liberal establishment.

That was part of the theme which Carter presented publicly yesterday, saying, "There are no hidden meanings in our commitment to human rights." Equally, Carter said he was attributing "no hidden meaning" to a Brezhnev statement of July that the Kremlin seeks by pursuit of detente to make peace in the 21st century "stable as never before."

While he pledged a search for deeper and broader "genuine accommodation" with the Soviet Union, however, the President reiterated every one of his objectives - declaring that "profound differences" between the two societies assure real competition along with cooperation.

This was intended, administration officials said, to overcome the illusion that there can be "a quick fix" through a resurgent "Spirit of Geneva" (or Camp David or Glassboro or Moscow) which can make basic antagonisms disappear.

Carter told the Soviet Union he does not seek to jettison the President Ford-Brezhnev outline of nuclear arms accord set at Vladivostok in late 1974, but to build on it.

he answer to Soviet worries "about our cruise missile" which have developed since Vladivostok, the President said bluntly, is a bargain which compensates for the American concern about "the buildup of Soviet strategic offensive weapons forces." Failure to deal with these real problems he said, "will only create an illusior of progress. . ."

Carter did not mention the impending Oct. 3 deadline on the existing U.S. Soviet limit on offensive strategic weapons, which U.S. planners expect to extend by agreement with Moscow He stressed, instead, the large collection of issues now on the U.S. Sovie agenda and the need to look beyond "sole preoccupation" with the military balance, to broader international is sues.

There are no new, specific proposal, by the President yesterday, administration officials acknowledged. To the Soviet Union, the President's reap prasal presents an option: It can be brushed off, assailed or invoked as an option for a new attemt to heal the bruses of the Carter administration's first experiences in dealing with what the President calls the "tough questions" below the surface of world diplomacy.