The nation's job picture worsened in June, the government reported yesterday, even though the unemployment rate fell slightly to 7.7 percent primarily because of a statistical quirk.

The number of jobs in the economy actually declined.

The figures came as the Federal Reserve Board, in recognition of the deepening recession, announced plans to dismantle between now and mid-August the remainder of the anti-inflation credit controls imposed last March 14. [Details on Page E1.]

The board said it will end the current restrictions on consumer credit and credit-card accounts July 23, and will begin even sooner to repeal restraints on bank loans. President Carter hailed the control as a success.

In the figures on joblessness, the Labor Department's montly survey showed the number of jobs in the economy plunged by 451,000 in June, while industry payrolls shrank by a hefty 514,000 jobs, the sharpest drop since late 1974.

However, the worsening did not show up in the jobless rate, because of a quirk in the survey procedure that inadvertently counted many students seeking summer jobs in the May unemployment figures instead of those for June.

The fact that the jobless rate did not surge sharply in June was expected to aid the Carter administration, at least in the short run, in its efforts to stave off a tax-cut stampede in Congress.

Officials conceded that had the unemployment rate jumped sharply, tax-cut fever would have intensified. The lawmakers went home yesterday for their July 4 and convention recess.

White House economists now expect the unemployment rate to rise to 8.5 percent or higher before finally peaking, but their feeling is that the slump in the auto and housing industries has about hit bottom and the jobless rate will climb more slowly.

However, Janet L. Norwood, the commissioner of labor statistics, cautioned that yesterday's report showed the economy's deterioration "has continued into June," and said, "Only time will tell whether that goes further."

AFL-CIO President Lane Kirkland warned that the June unemployment figure masks the worsening picture. He reiterated labor's call for more antirecession job programs, rejecting both tax cuts and further budget-balancing.

Meanwhile, sources disclosed that Democrats on the House Ways and Means Committee, in a caucus on Wednesday, indicated they are privately opposed to a tax bill this session, but will go ahead with hearings anyway on July 22.

Both the Ways and Means panel and the Senate Finance Committee have scheduled sessions on the tax-cut issue for that week. However, Ways and Means so far has agreed only to consider whether to draft a bill this year, not actually to do it.

The jobless rise in June brought the overall number of unemployed Americans to just over 8 million, up 148,000 from May. And a growing proportion of the new joblessness resulted from layoffs rather than voluntary separations.

As has been the case in previous months, the bulk of the rise in joblessness was concentrated in the manufacturing sector, particularly in durable goods industries, which are most affected by the auto slump.

However, the June report showed job layoffs spreading for the first time into the service industries as well, with sizable job losses posted in wholesale and retail trade. Overall hours worked also declined.

Nevertheless, the jobless rates for most categories of workers' remained essentially unchanged in June, and the teen-age jobless rate fell to 18.5 percent, from 19.2 percent in May, largely because of the sampling quirk.

There also are sharp differences in jobless rates among various states and regions. The unemployment rate in Michigan dipped to 14.1 percent in June, from 14.4 percent the previous month.

At the same time, the jobless rate for Texas, which had been at 5.4 percent in May, edged up to 5.5 percent in June. California's jobless rate jumped to 7.3 percent, from 7.1 percent before.

With the June drop included, the economy now has lost some 1.4 million jobs since the recession took hold in earnest last February. However, the downturn is not yet as bad as that of 1974-75.

The Fed's action in dismantling the remainder of its credit controls had been expected for several weeks. With loan demand down sharply in the face of the recession, the restraints had little practical effect anymore.