Mayor Marion Barry, facing growing criticism of his handling of the city government yesterday warned blacks against criticizing other blacks now in power, like himself, who are grappling with problems of long standing.

Addressing the 1980 graduating class of the University of the District of Columbia, Barry said, "Let us not use the fury and anger we feel toward society and injustices and turn it against each other."

"I an concerned that as blacks become leaders in positions where they weren't before, that other blacks begin immediately to criticize everything that's there and act as though [the problem] started when we got there."

Barry has been criticized in recent weeks by many blacks in Washington -- including some old supporters from his activist days -- for proposing to cut back funds for the public schools, Medicaid, summer jobs and recreation programs while not cutting deeply enough into the city bureaucracy, which critics in Congress and elsewhere charge is wasteful and inefficient.

Barry has drawn particular rebuke for his government's failure to describe accurately the extent of the city's financial problems. Initially, the city reported an anticipated budget deficit of $29.6 million. But in a matter of weeks, the figure grew to $172 million. Some city officials still say they are uncertain about the true amount.

Last week, the mayor was booed on the steps of the District Building by angry city employes and activists protesting his proposed budget cuts. At one point, Barry told some who kept interrupting him, they could "go to hell."

Barry, who gained public attention and later power in this city through marches, demonstrations and militant street activism, told the 1,000 students graduating from UDC yesterday, "It doesn't take much courage, much guts or much brains, quite frankly, to march down to the District Building against me."

Addressing the students as "brothers and sisters," Barry said the city's budget problems did not begin with his administration, but started about 10 years ago.

"Congress is responsible for most of what we're in," he declared, hammering away at a theme he has employed several times in recent weeks since his management of the city's finances has come under attack.

"Some of you might say, 'No, that's not true.' And someone else might come along and say, 'How do you know that's not true?' and you might say, 'I read it in the newspapers or I heard it on television.'"

". . . This is not to say you shouldn't read the newspapers," Barry added, but stressed that students should draw their own conclusions about the city's problems.

Barry, speaking in the stuffy, dimly lit D.C. Armory, received polite, but unenthusiastic applause from the graduates. As part of his new austerity program, the mayor has recommended cutting $1 million from the university's current-year budget.

The school has already had to cut back on summer classes, purchases of equipment and building repairs. There is a freeze on hiring and UDC is also considering delaying its opening next Septemeber to cut costs.

The graduates applauded Barry three times during his speech, but only once vigorously -- when he endorsed the proposal for a second UDC campus on Mount Vernon Square downtown. Congress has held up funds for the construction of that campus for the past five years, suggesting that the university expand its campus on upper Connecticut Avenue.

Perhaps the lightest moment in Barry's speech came as he was being introduced. University President Lisle Carter called him "the man leading us in these difficult times -- the mayor of New York."

When Carter quickly corrected himself, Barry smiling, took the podium and quipped, "I have enough probelms with Washington. You can keep New York."

Many students responded positively to Barry's speech afterward. For public management major Simon Woodard, the mayor's appeal for blacks not to criticize other blacks struck a chord.

"It's a pattern I've observed.It's almost like blacks don't have confidence in their own people. They're too quick to point the finger without having all the facts," Woodard said.

"Even though there is a black mayor and the majority of the City Council is black and there are quite a few blacks in major positions, there is a lot of opposition to them," said Betty Washington, an accounting major who has worked in the D.C. government.

"I feel this might lead to the city reversing itself [to a majority white government] again," she added.

"I think it's something for students to think about -- who's to blame" for the city's financial problems, said Essie Williams. "But I think (the mayor) is definitely responsible for correcting this."

While Barry was speaking at the armory, Judge A. Leon Higginbotham Jr. of the 3rd Circuit Court of Appeals addressed Howard University's 2,000 graduates under sunny skies in the university's outdoor stadium.

The 52-year-old Higginbotham was enthusiastically received by the students. He was the first black man named to a federal regulatory commission and at age 35 became one of the youngest men to be named to the federal bench in recent years. He stressed Howard's long histroy in educating blacks and hiring black scholars when many of America's foremost universities would not accept them.

Higginbotham, a towering man well over 6 feet who had to stoop to receive the academic hood for his honorary degree, also praised Howard for achievements in civil rights and public health.

"But for Howard, thousands of black babies would have died unnecessarily. But for Howard, thousands of forums would not have had articulate minority spokespersons . . . But for Howard, thousands of Africans would not have received the academic options which allowed them . . . to ultimately assume positions of world leadership."

Using a quote he took from the editors of Freedom's Journal, the first black newspaper in the United States, Higginbotham reminded the students, "We must plead our own cause. Too long have others spoken for us."

"Whether most Americans like it or not, they must face up to the stark reality that the destiny of the world will no longer be shaped exclusively by persons with white skins," Higginbotham said.

Both Higginbotham and Barry told the students that because blacks have made significant advances in recent decades, they must not forget there is still work to be done.

"Don't ever get so far removed from the problems," Barry said, "that you become the problem."