U.S. automakers made impressive sales gains in the waning days of 1982, but the figures weren't good enough to keep last year from being the industry's worst in 20 years.

The five domestic manufacturers sold an estimated 448,048 cars in December, a 25.3 percent increase over 357,580 cars sold in December 1981. But annual sales dropped 7.2 percent from 6.25 million cars sold in 1981 to 5.75 million last year, the worst sales performance since 1961, when U.S.-based manufacturers sold 5.54 million cars.

"It wasn't a great year," said Robert C. Stempel, general manager of General Motors Corp.'s Chevrolet Division. "But it was important that we closed with something of a bang. We're looking for a good 1983." Stempel joined other auto executives here yesterday at the opening of the 41st National Capital Area International Auto Show.

Edsel Ford III, scion of the founders of Ford Motor Co. and marketing director of the company's Ford Division, agreed that 1982 was a bad year. But he said the domestic industry's record in the Dec. 21-30 period, the last nine selling days of 1982, was strong enough to support a recovery.

U.S automakers sold 161,823 cars in the late-December period, a 27.8 percent increase over 126,602 sold in same period in 1981. "That means we finished the year at an annual selling rate of about 8.9 million cars. That's not great. But it's not bad, either," Ford said.

Auto industry analysts, however, were more restrained.

"If we have a good January, I could become a believer" in the talk about a gradual recovery, said David Healy of New York-based Drexel Burnham Lambert Inc.

"It was sort of a contest closing period, during which many customers thought they might be able to purchase 1982 cars at the cheapest possible prices. That does not necessarily mean a recovery. It's just too early to be certain," Healy said.

But hope is the hardy perennial in the auto business, and the flower was in full bloom yesterday at the auto show's opening. Dealers mingled with manufacturing executives, patting backs and basking in the metallic glory of all that glittered on the huge showroom floor. Happiness is customers in the auto business, and there were a goodly number of potential customers on hand yesterday, gently kicking the wheels, touching the metal, and squeezing the leather seats of some luxurious interiors.

GM's Stempel was beside himself with joy. "This is the kind of thing we need--enthusiasm," he said.

The company-by-company annual sales figures show a need for something. GM sold 3.51 million cars in 1982, down 7.4 percent from an already low 3.79 million cars in 1981; Ford, the second largest automaker after GM, was off 2.5 percent, from 1.38 million in 1981 down to 1.35 million in 1982; Chrysler Corp. was off 5.2 percent, from 729,873 cars sold in 1981 to 691,703 sold last year; American Motors Co., now a partner with Renault of France, was down 17.7 percent, from 136,682 cars sold in 1981 to 112,433 sold last year; and Volkswagen of America was way down, 43.7 percent, from 162,005 cars sold in 1981 to 91,164 sold in 1982.

The December figures were better for all, except VWOA. AMC, for example, said it sold 13,757 cars last month, a 77.7 percent increase over 7,741 sold in December 1981; Ford sold 110,578, a 53.5 percent increase over 72,036 in the year-ago period; Chrysler was up 26.9 percent, 60,954 compared with 48,045 in December 1981; GM was up 17.4 percent, 256,728 compared with 218,670 in the year-ago period; and VWOA was down 45.6 percent, from 11,088 in December 1981 to 6,031 last month.