General Motors Corp. yesterday issued final sales figures for 1981, its worst since the deep recession of 1975, while Chrysler Corp. wound up the year with an 11 percent gain in sales of its U.S.-built models compared with 1980.

Ford Motor Co., American Motors Co., and Volkswagen of America are expected to report their final 1981 figures this week, leaving the industry with its poorest sales performance since 1961, when a recession and a strike against GM undercut sales severely. The 1981 total will be about 5 percent below 1980's disastrous level, when the U.S. automakers lost $4.2 billion. The dollar loss in 1981 is expected to be about $1.2 billion, thanks to severe layoffs and other cost-cutting by the four largest domestic auto companies.

GM's auto sales for 1981 totaled 3.79 million, 7.8 percent below the 4.12 million total in 1980, based on daily sales averages. Chrysler, which kept its rebate program in place after GM and Ford Motor Co. ended theirs, reported 1981 auto sales of 729,873 compared with 660,017 in 1980.

Both companies were headed downward at year's end, as December car sales sank virtually out of sight. GM's car sales for the month were down 19.6 percent from December 1980, while truck sales dropped 19.3 percent from the year before despite GM's introduction of a compact truck line, the Chevrolet S-10.

GM is hoping to revive its car sales with the introduction this month of a new line of front-wheel-drive, intermediate-sized cars, and redesigned Chevrolet Camaro and Pontiac Firebird sports cars. It is spending $4.5 million on a sweepstakes competition to attract potential buyers to GM showrooms without saddling the company with the heavy expense of a rebate program.

Chrysler said its December car sales, including Japanese-made subcompacts sold under Chrysler's name, totaled 48,045 compared with 63,127 in December 1980. Truck sales for December were 15,292, up 10 percent from the 13,933 total in December 1980.

In maintaining its rebate program, Chrysler has deliberately sacrificed profits in favor of sales to keep the company's cash flow from drying up. Chrysler officials say they have sufficient cash to continue operating well into the new year, although some analysts believe Chrysler may have to sell its profitable Chrysler Defense Division, which produces tanks for the U.S. Army, if a recovery in auto sales is not under way by late spring or early summer.