Justice Department attorneys, who lost their antidiscrimination case last April against Fairfax County in federal district court, yesterday asked the U.S. Court of Appeals in Richmond to overturn the decision.

In a 59-page brief, the department said U.S. District Court Judge Albert V. Bryan Jr. made major errors in rejecting charges that Fairfax systematically discriminated against blacks and women in hiring for county government jobs.

Bryan issued his ruling in April after a three-day trial in Alexandria.

Although be upheld the county's contention that it committed no widespread discrimination, Bryan agreed with the Justice Department that statistical data showed discriminaton against blacks in police, fire, and maintenance jobs in 1976 and 1977. He said there was discrimination against women from 1974 through 1978 in hiring truck drivers and manual laborers.

But Bryan praised the county's own affirmative action program, adopted in 1978, as "vigorous and successful." Thus, he said, no court decree was necessary about hiring blacks. He issued a general decree barring discrimination against women in blue-collar jobs, but said no court order with numerical hiring goals was necessary.

In its appeal, the Justice Department said the evidence it presented at the trial showed a much wider patten of discrimination than Bryan found. It asked the appeals court to require Bryan to issue a sweeping decree that would establish detailed numerical goals for promoting blacks and women and would ban the civil service exams the county uses to test potential employes.

Even if the appeals court judges agree with Bryan that discrimination was limited, the Justice Department said he should be required to set strict hiring goals in the particular job categories affected and also allow individuals to collect money damages from the county.

Yesterday, Jack Gould, the assistant county attorney who argued the case for Fairfax, said the county will file a reply brief in about a month. $"We were convinced that what we were doing was correct," Gould said, "and we were upheld by a judge after a trial. We will keep on doing it."

Attorneys for both sides said an oral argument before a three-judge panel in Richmond probably will not take place until spring, and that a decision is not likely until late summer.