Walter F. Mondale tonight accepted his overpowering defeat with a touch of sadness but with grace, saying he was "at peace with the knowledge that I gave it everything I've got."

Mondale congratulated President Reagan, and thanked Americans "for hearing my case." Privately, he told his closest supporters that the next two years will show that he was right.

Mondale, his family standing behind him, conceded defeat and told 3,000 fellow Minnesotans, "He has won. We are all Americans. He is our president, and we honor him tonight."

He said the American people had made their choice "peacefully, with dignity and with majesty. And although I would have rather won, tonight we rejoice in our democracy. We rejoice in the freedom of a wonderful people and we accept their verdict."

To the young campaign workers who so often yelled "no" whenever he acknowledged the Reagan victory, he said, "I know how you feel because I've been there myself. Do not despair. This fight didn't end tonight. It begins tonight."

Mondale was a lonely native son in defeat tonight. Few of the state's top Democrats shared the stage with him, and some local Democratic officeholders shook their heads in disappointment at the size of the crowd.

But Mondale, born in rural Elmore and tutored by Hubert H. Humphrey in liberal Midwestern Democratic tradition, said he was proud of his state.

He praised Minnesota, which may have saved him from embarrasment. Late returns showed Mondale leading in his home state.

He offered special praise for Geraldine A. Ferraro, his running mate, the first woman on a major party ticket in a national race. "We're very proud of Gerry," Mondale said. "We didn't win, but we made history, and that fight has just begun."

Mondale was stoic throughout the day, but afterward, as he left the stage and entered a holding room, he turned for a glance at a few reporters and aides, his eyes reddened and wet.

Earlier in the evening, Mondale met briefly with supporters and staff, telling them, "I know that you did this because you believe in America." He then retired to his hotel suite to watch televised returns with his family and senior staff members.

He dined on cheeseburgers, his favorite campaign meal through his years of striving for what became an illusive goal.

"I would describe the scene as quiet," campaign press secretary Maxine Isaacs told reporters. "It is not a very weepy scene at all, just quiet."

Mondale also placed calls to his strongest supporters, including New York Gov. Mario Cuomo, who gave the keynote speech to the Democratic National Convention and who was considered early on as a Mondale running mate.

Cuomo quoted Mondale as saying, "The next two years will show how right we were. I'm not sure I should be happy about that."

As television networks projected a landslide victory for President Reagan, a somber mood prevailed among the handful of Mondale aides sitting in a staff room at the St. Paul Radisson Hotel. The calm was broken slightly by brief applause as one network projected that Mondale would win his home state, Minnesota.

Mondale attended a staff party with several hundred persons, including about 150 from the central campaign office in Washington who flew up for what was to be a victory celebration.

The party was closed to the press, but one person who attended told reporters that Mondale had told the crowd, some of them in tears, "I know that you did this because you believe in America. You've learned more in the last year and a half than most people do in a lifetime."

Mondale had returned to his home town to hear the people's verdict, telling his fellow Minnesotans he had given "everything I've got" to his quest for the presidency. Mondale voted with his family near their home in suburban North Oaks early yesterday.

Mondale had been in an unusually upbeat mood for much of the final days of the campaign.

At an Election Day breakfast with family and friends, Mondale was in "a very, very upbeat mood, really very peppy," said former attorney general Warren Spannaus, who attended.

The end of his long campaign came about eight hours before he cast his ballot. The family -- wife Joan and children Ted, Eleanor and William -- stood behind him in an old hangar at the Minneapolis-St. Paul International Airport where thousands of Minnesotans crowded in to welcome him.

Mondale, his face drawn, his emotion slow to surface, was interrupted on two occasions by a lone, persistent heckler. But with his feet planted once again in Minnesota soil and his heart in familiar surroundings, he said, "Tonight, I end what may be the longest campaign in American history.

"For thousands and thousands of miles, through long days and long weeks and long months -- now long years -- through all the debates, through all the campaigns and speeches, through all of the joys and heartaches, I could hear you, and I could also hear Hubert Humphrey pushing me on.

"And I'll tell you this: Whatever the result . . . I've given this campaign everything I've got to win."

"For 22 months," Mondale said, "I've traveled all over this country. But I never really left Minnesota because I've been talking to America about Minnesota values. . . . All that I know and learned, I learned in our state.

"All that I am and all that I believe flows from what I have learned from you . . . . You have trusted me all these years. And you have given me, a small-town boy from Elmore, a chance to shape our country and to shape our times. And you have given me a life that is very, very rare and marvelous.