Office of Management and Budget Director David A. Stockman stoutly defended President Reagan's new budget yesterday against the charge that it is unfair to the poor, saying the "process of curbing spending growth has been carried out with reason and . . . full awareness of the legitimate claims of the needy, the old, the unemployed."

In a speech to the National Press Club, Stockman complained that "essentially false impressions" have been given of the budget in the press and elsewhere, and went on to give his most detailed defense to date of the administration's record on the fairness issue.

In essence he said that while Reagan has proposed cuts in domestic programs these are small when seen in context and would still leave social spending far higher, in real or after-inflation dollars, than it was in 1970, after enactment of Lyndon B. Johnson's Great Society.

Domestic spending in Reagan's 1984 budget, excluding interest on the national debt, "is down 4 percent from 1981, but it is 95 percent higher than in 1970," after taking account of inflation, Stockman said.

"Yes, there are cuts and savings in this budget--but, compared to 1983, the differences are marginal . . . and compared to 1970, the 1984 Reagan budget makes the Great Society funding levels . . . appear positively antediluvian," the budget director said.

Stockman concentrated entirely on the domestic spending side of Reagan's budget and did not deal with either defense or taxes. He also sought to separate the budget cuts from the effects of the recession.

"No one, from the president down, is disputing that this lengthy recession has caused suffering," he said.

Chiding the press for giving space to what he called "trumped-up sensationalism" and "careless charges" about the budget, Stockman took as his starting point the total spending Reagan is now proposing for domestic programs, excluding interest, pointing out that of this "one-half trillion dollars . . . $424 billion is for transfer payments checks sent out to individuals and social programs."

If all of this money were spent on the 65 million people who are elderly, poor or unemployed it "works out to $6,500 per capita . . . . There is plenty of room for programmatic arguments . . . but gross inadequacy of total dollars is not evident in these totals," he said.

He went on to reject some specific critical analyses of Reagan's program. A recent study by the Food Research and Action Center pointed to a rise in infant mortality in some states and areas and was cited in the media, including in The Washington Post, as evidence that Reagan budget cuts were hurting national health.

Stockman pointed out that for the nation as a whole statistics actually show a continuing decline in infant mortality in 1981 and the first 10 months of 1982. He said there have been deviations from this trend in scattered states every year, but all states have been down over the long run.

He also took specific issue with an analysis by the antipoverty Center on Budget and Policy Priorities and staff of the House Budget Committee, which said Reagan's budget would lead to a 19 percent after-inflation spending cut in programs for poor people. This too was reported in The Washington Post and elsewhere.

Stockman said most of the cut was a rescission of old budget authority to stop further expansion of housing assistance and that "not one dime of this" would reduce the actual spending level in 1984.

"When you correct the analysis for this distortion," Stockman said, "even the Budget Committee staff, which are not noted fans of ours, conceded that the reductions in program outlays would only be $1.4 billion or 2 percent." And counting only "the cash and in-kind assistance programs that form the core of assistance to the needy," spending rises half a billion dollars to $66 billion, he observed. In some cases Stockman claimed credit for spending increases that Reagan has tried to block. Housing was one example; he noted that an estimated 11.6 million people will be living in subsidized housing in 1984 as against 10.9 million in 1983.

This is mainly because of commitments made in the Carter years and before that Reagan has sought to curtail. He also noted that spending will rise on the program that helps feed needy women, infants and children (WIC). That is because of congressional action; Reagan has tried to cut WIC spending the last two years.

Stockman also said that much of the money spent under means-tested programs ostensibly for the poor actually goes to families whose incomes are 150 percent of the official poverty line or higher.

In 1981 that 150 percent figure was $13,930 for a family of four, he noted. Many administration cuts have been to refocus these programs more toward those at the poverty line and below, he said.