Former Federal Reserve Board chairman Arthur F. Burns, a member of President Reagan's committee of private economic advisers, yesterday publicly criticized "the resolution of the admittedly difficult automobile import problem" by acceptance of so-called voluntary quotas set by the Japanese government.

In a speech at Xavier University in Cincinnati, Burns said that the auto decision was not in accord with the general anti-inflation program outlined by a committee of prominent citizens just before President Reagn took office.

Burns, who now is a senior scholar at the American Enterprise Institute here, also said that the Reagan-Kemp-Roth tax cut "is larger than most committee members had contemplated."

Burns' comment on the auto-import question was somewhat guarded but nonetheless the most specific public criticism by anyone connected with the Reagan administration of the arrangement brought back from Tokyo by U.S. Trade Representative William Brock under which Japan will undertake to reduce its auto shipments in the next 12 months by 140,000 cars.

Office of Management and Budget Director David A. Stockman acknowledged on "Meet the Press" last Sunday that the auto deal "deviates. . . in some degree" from a "purely theoretical" free-trade concept. But basically, "what we have to focus on is the practical result," Stockman said. "The practical result is that there will be very little change in the composition of the domestic market."

Officials such as Council of Economic Advisers Chairman Murray L. Weidenbaum -- who originally opposed any sort of quota arrangement, voluntary or otherwise -- have felt constrained to defend the Brock agreement. When asked during an appearance in New York Tuesday evening how an administration believing in supply-side principles could defend a reduction in car imports, Weidenbaum responded:

"One wag said that the next Nobel Prize winner will be the young man who succeeds in explaining how restricting imports supports supply-side economic theory. But seriously, a truly undesirable policy has been avoided. The administration didn't negotiate an orderly marketing agreement. The Japanese of their own volition decided to restrain exports, and I am not presumptuous enough to explain to the Japanese what they should do."

Privately, many prominent Reagan administration officials are much more critical of the decision. Many top officials think it was a serious mistake to depart from free-trade principles, fearing the auto deal will trigger protectionist actions elsewhere. In addition, some of Reagan's outside economic advisers think that the president's refusal to stand firm against quotas has hurt his credibility.

In his speech yesterday, Burns gave the administration credit for pursuing other steps that has been endorsed by his Committee to Fight Inflation.

He noted, on the other hand, that the administration so far has opposed any modification of the automatic cost-of-living adjustments for Social Security benefits -- one of the committee's key recommendations. But he expressed the hope that Congress will act on its own to reduce "this costly burden" to the federal budget.

Burns also said that he maintains a general feeling of optimism on chances for beating back inflation primarily because congressman in both political parties appear to be willing to support large budget cuts. "Nevertheless, it is not entirely clear as yet whether the American public has sufficiently mastered the lesson taught by recent history to be willing to accept the discomfort of a stern anti-inflation policy," Burns said.