Saudi Arabia, which is paying at least six Washington public relations and law firms roughly $1.5 million a year for advice and influence, discovered this week how limited the kingdom's once powerful lobbying machine has become.

The lopsided votes in Congress -- 73 to 22 in the Senate and 356 to 62 in the House -- against a relatively modest $354 million missile sale contrasted sharply with previous Saudi successes and lobbying tactics.

For example, the main Saudi point-man during the controversial debate in 1981 over whether to sell Riyadh U.S.-made Airborne Warning and Control System (AWACS) planes, Saudi Ambassador Prince Bandar, was back home during the crucial 50-day period prior to this week's floor action, returning to Washington only on the night of the Senate vote Tuesday.

"There has got to be somebody here who is a Saudi speaking for the Saudi government," complained one frustrated lobbyist, who asked to remain anonymous.

By contrast, in 1981 Bandar was given an office in the Capitol by then-Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) to facilitate Saudi lobbying for an $8.5 billion arms package. Bandar also participated in White House strategy sessions.

While Congress was voting to reject the latest package, the chief administration lobbyist -- President Reagan -- was at the Tokyo summit. Reagan, who actively worked for the 1981 Saudi sale, has been preoccupied with the White House campaign against Libyan leader Muammar Qaddafi and with the controversial $100 million aid package for the rebels fighting the government of Nicaragua.

"The White House was supposed to take the lead on lobbying Congress," another disgruntled lobbyist for the Saudis said. "The consistent message from senators was, 'Where is the White House?' "

In the absence of Bandar and Reagan, the U.S. firms hired to defend Saudi interests here were left to carry the fight to Capitol Hill in the face of congressional anger at Saudi support for Libya. Some lobbyists even suggested that this week's defeats raise questions about the real power of high-priced Washington public relations firms in their representation of foreign embassies.

At least six firms, with contracts ranging from $50,000 to $500,000, now work for the Saudi embassy to help with various aspects of "representation" here, from lobbying on the Hill to providing advice on the news media and other American institutions.

Four of them -- the Hannaford Co. Inc.; Cook, Reuf & Associates Inc; attorney Paul J. Manafort; and Berman, Bergner & Boyette Inc. -- were involved in trying to persuade Congress to approve the missile sale. Those four firms collectively will be paid $690,000 for their services, according to Justice Department foreign agent registration records.

Hannaford took the lead in preparing literature advocating the sale. The firm produced a glossy, 20-page background paper, "Deterrent Action by the United States for Protection of the Oil-Critical Persian Gulf Area Through the Sale of Military Equipment to Saudi Arabia."

Every Senate office got a copy, with a seven-page list of answers to the question, "What has the government of Saudi Arabia done to advance 'basic American foreign policy objectives' in the Middle East?"

The most recent Washington public relations firm to enter Saudi service, Michael K. Deaver & Associates, which has a $500,000 contract, played no visible role in the pro-Saudi lobbying effort, according to representatives of several of the other firms.

"Deaver has done absolutely zero," one of them said. "But his involvement might have been counterproductive anyway," he added, referring to the controversy surrounding the former White House deputy chief of staff who is under investigation for possible violation of federal conflict-of-interest laws.

"I can't comment on what we do for a client," a spokesman for Deaver's firm said. "I have no information on the arms sale."

Another well-known firm representing Saudi interests here, Dutton & Dutton, is paid $300,000 annually by the Saudis but also was absent from the arms lobbying fray. Fred C. Dutton said he never lobbies for the Saudis on the Hill and was away for the past five weeks in Europe and Saudi Arabia on other business.

Dutton said the Saudi government had taken the position that "this is the administration's arms sale proposal and not what they wanted."

"The decision was, the administration should take the responsibility for it in the present [political] climate," he said.

Nonetheless, four firms appeared to be actively working for the Saudis on the issue. Berman, Bergner & Boyette Inc., a new company with a three-month, $50,000 contract, was hired two months ago by the Saudis expressly to lobby on the arms proposal.

One of its Republican partners, Jeffery T. Bergner, is an old hand with the intricacies of the Senate, having recently left his post as majority staff director of the Senate Foreign Relations Committee.