A leading civil rights lobbyist voiced strong criticism yesterday of President Carter's record on race relations and other domestic issues since taking office.

In a kind of state-of-the-union message on civil rights, Clarence M. Mitchell Jr., Washington director of the NAACP, charged that "there are no black faces in Carter's inner circle. It's an almost parochial arrangement. Your birthplace in Georgia determines your place in the inner circle.

"This is not good," Mitchell added. He urged that Carter adopt "the same openness" in domestic decision-making that he has shown on some foreign policy issues and that he include "a person of real stature on civil rights in his inner circle."

A White House spokesman declined to comment on the speech except to say that Martha Mitchell, a presidential assistant who is no relation to the NAACP leader, is black and among other things, keeps lines open to the black community. She is highly regarded by the President, the spokesman said.

Clarence Mitchell is also chairman of the Leadership Conference on Civil Rights, a coalition of 137 civil rights, labor, religious and civic groups. As Washington representative of the NAACP, he has lobbied for - and written parts of - every major piece of civil rights legislation in the last 30 years.

In his evaluation of Carter before the Washington Press Club yesterday, Mitchell found things to praise.

"His sensitivity to the poor, to blacks is a great asset," Mitchell said. The civil rights leader applauded Carter's appointment of Patricia Roberts Harris as Secretary of Housing and Urban Development, Clifford Alexander as Secretary of the Army, and Eleanor Holmes Norton as chairman of the Equal Employment Opportunity Commission. All are black.

Mitchell also commended Carter for his concern for human rights in other nations and his announcement that the Pentagon will consider upgrading certain undesirabto Vietnam war veterans.

But the bulk of his evaluation of Carter was critical, and although he said the administration "still has a good reservoir of confidence among black voters," the tone of his speech was one of disappointment.

"The administration's position on the minimum wage is one unfortunately colored by the Southern concept of what constitutes a good salary," Mitchell said. "It's colored by a kind of negative attitude on paying people a decent wage" in the South, he charged.

Carter told Congress last week the administration would support a 20 cent increase in the minimum wage, now $2.30, instead of the 70-cent increase favored by organized labor.

Mitchell said Carter and his aides don't realize the cost of living is higher elsewhere in the country than it is in the South.

Asked about school desegregation, Mitchell said Solicitor General Wade H. McCree and Assistant Attorney General Drew S. Days III, both blacks, have said they believe some federal judges have gone too far in ordering extensive busing to offset segregation.

"It's simply not the truth," Mitchell said. "Busing is an appropriate remedy if a judge finds unconstitutional segregation."

Mitchell repeated his earlier criticism of Carter for choosing Griffin B. Bell as Attorney General and Peter F. Flaherty as deputy attorney general. "It was a calamitous error to put in the Department of Justice in top positions persons of questionable civil rights records," Mitchell said.

He also said it was "very shortsighted" of Carter to fail to resubmit the nomination, made by President Ford, of Thaddeus J. Garrett Jr. to the Consumer Product Safety Commission.

Arguing that Garrett, who is black, is a "bright young man," Mitchell said Carter's action is "a slap in the face to blacks" who didn't think of party politics when they supported his election.