Fairfax County supervisors yesterday rejected a plea by Board Chairman John F. Herrity to press for a revision of Northern Virginia's regional gasoline tax, ignoring his claims that the tax is "unfair" to the county's motorists.

By a 5-to-4 vote, the supervisors refused to register a protest over the tax's allocation formula, which they had relunctantly accepted last winter in the belief that it was the only Metro revenue bill that Virginia General Assembly would approve. The vote was a setback for Herrity, the country's top elected official, who earlier this month called a press conference to announce he had the support of two senior Fairfax legislators who were going to seek revision of the tax during the next assembly session.

Supervision Joseph Alexander (D-Lee) yesterday led the fight against Herrity's plan, cautioning that a reversal of the board's earlier decision would only arouse anger in a state legislature that is generally not sympathetic to Northern Virginia.

"If we ask them for a revision, they'll all say, 'Here come those idiots from Northern Virginia again," said Alexander, who voted with the majority when the Northern Virginia Transportation Commission fixed the funding formula earlier this month. Should the issue be returned to Richmond, Lee said: ". . . We would stand a good chance of getting nothing back or getting this repealed."

Funds from the regional tax, which adds 2 percent to the price of a gallon of gasoline in the northernmost Virginia suburbs, are to be used to help the localities pay their rapidly rising Metro bus and rail bills. It is estimated that the tax will raise $11 million a year at the current rate, and more than twice that amount when an additional 2 percent is added to the rate in mid-1982.

Herrity argued that Fairfax, which accounts for approximately 60 percent of gasoline tax revenues, should receive a comparable share of the tax's benefits. Instead, he said, Fairfax gets only 50 percent of the tax, forcing county motorists to underwrite the Metro costs of neighboring jurisdictions.

"We have more than 60 percent of the land mass, more than 60 percent of the population, and more than 60 percent of the vehicle miles. More than 60 percent of the rush-hour transportation problems by 1990 will be in the county," Herrity said. "Based on any criteria you can name, this money should stay in Fairfax County."

According to estimates by Supervisor Thomas M. Davis (R-Mason), who supported Herrity, the county will pay approximately $15 million more in gas taxes than it will receive in benefits over the next five years.

Supervisor Sandra L. Duckworth (D-Mt. Vernon) rejected Herrity's asertions that Fairfax is entitled to a bigger piece of the tax pie, pointing out that the county has a disproportionately large number of service stations. "It is not logical to assume that all of the gas purchased in Fairfax County is used in Fairfax County," she said, urging the supervisors to cooperate with other area jurisdictions.

"If we ever expect to get anything in Fairfax County, we must believe in the regional concept," said Duckworth.

Voting with Alexander and Duckworth to reaffirm the current allocation formula were Supervisors Marie B. Travesky (R-Springfield), Martha V. Pennino (D-Centreville), and James M. Scott (D-Providence). All five are Fairfax representatives to the transportation commission.