Chrysler Corp. yesterday reported that it lost $1.71 billion during 1980. It was the largest annual loss ever for an American company.

But the huge deficit had been expected, and was somewhat offset by other, generally good news for the beleaguered auto maker yesterday.

As expected, the government's Chrysler Loan Guarantee Board authorized the No. 3 car maker to begin the sale of $400 million in federally backed bonds, giving Chrysler an infusion of badly needed cash it has been waiting for since December.

And, despite its record deficit, the company showed success in trimming its losses through the year, as it scaled back its payroll and plant facilities severely.

The deficit for the last three months of 1980 was $235 million, and the cash loss from operations was significantly less: $157 million. The fourth-quarter figure was less than the loan board's staff had predicted, and was Chrysler's smallest quarterly deficit since the spring of 1979.

Chrysler's report closed off the worst financial year ever for the U.S. auto industry. The $1.71 billion figure topped Ford's 1980 losses of $1.54 billion, the previous record. General Motors Corp. lost $763 million, and American Motors Corp. had a $198 million loss.

The final approval of the loan guarantee by the Chrysler loan board permitted the company to begin selling 10-year notes with a 15.31 percent yield to investors, with repayment guaranteed by the government, which has the first claim on Chrysler's assets.

Treasury Secretary Donald T. Regan yesterday indicated that the government's generosity toward Chrysler may be at an end. Chrysler, which borrowed $800 million in guaranteed loans last year and now is getting $400 million more, still could draw down a final $300 million, according to the aid plan approved by Congress.

But Regan said it is "now clearly the sole responsibility of Chrysler's senior management to achieve or exceed the results projected in the company's operating and financing plans."

Chrysler Chairman Lee A. Iacocca has told reporters the company doesn't plan to ask for the final $300 million.

Since December, Chrysler has improved its competitive position against the other American manufacturers with a rebate program worth more than $500 per car on most of its models.

Its share of the U.S.-manufactured car market jumped from under 9 percent during most of 1980 to 11.4 percent in February, and, in response, both GM and Ford have begun rebate programs.

Yesterday, Chrysler announced a new sales incentive plan to give new car buyers a 7 percent rebate on sales prices through next Tuesday, and a 6 percent rebate after that. Its original rebate plan was tied to the prime lending rate, which at most banks has dropped to 19 percent from the December peak of 21.5 percent.

Despite its stronger recent showing against the other U.S. car makers, Chrysler's recovery is not assured. The rebates are cutting into badly needed profits, and sales are still below the levels that Chrysler and the government believe must be reached if the company is to return to profitability.

Iacocco told Chrysler shareholders yesterday that the company had had "every reason to believe" it would earn money in the fourth quarter, "but a series of unexpected events suddenly devastated the U.S. car market," referring to the sudden jump in interest rates that crippled car sales.

Chrysler officials say they believe a recovery is certain if the prime lending rate declines to the 15 percent level. In the operating plan approved by the loan board, Chrysler has set a goal of capturing 9.1 percent of the market for U.S.-built cars, which it hopes will reach 9.6 million units this year.

By necessity it has become a smaller, leaner company, cutting its hourly work force in this country from 96,000 two years ago to 50,600, and its white-collar payroll from 40,000 to 23,000 in the same period. Seven plants have been closed, and the company has turned increasingly to purchased components rather than building its own.

To qualify for the $400 million in new loans, Chrysler had to win concessions from employes, suppliers and lenders totaling more than $1.2 billion. The United Auto Workers agreed to give up $622 million in wage and benefits, and $161 million is to come from nonunion employes.

Suppliers agreed to take delayed payment on $72 million in past-due bills, and in the final key concession 150 lenders approved a new financing plan that wipes off $1.1 billion in debt in exchange for preferred stock and a $67 million cash payment by Chrysler.

These steps have enabled Chrysler to reduce its financial break-even point to 1.2 million cars and trucks, half the figure in 1979, before the cutbacks began.

But it reamins dependent upon a revival of the overall market for American-made cars, which the industry is hoping to see begin next month.