Mondale conceded Wednesday morning after the vote count showed him trailing by 2 percentage points with nearly 99 percent of the vote counted.
"It appears that this election has been decided and a few minutes ago I called Senator-elect Norm Coleman ... and to wish him the best," Mondale told a crowd of supporters who cheered, "Fritz, Fritz, Fritz." "I told him what I really believe that the U.S. Senate is the best job in America.
"This has been one of the most unbelievable moments in Minnesota history and perhaps in U.S. history -- to begin this campaign in the saddest of moments. ... It was wonderful."
Mondale entered the race Thursday, an emergency replacement for Wellstone who died in a plane crash just 11 days before Tuesday's election.
"The wave is moving from east to west and we're waiting for it to hit Minnesota," Coleman told cheering supporters late Tuesday. "When you see the energy in this room, you know the future is in and with the Republican party."
The whirlwind campaign was highlighted by Monday's debate between the two candidates. Mondale, 74, often sounded like he was lecturing the younger Coleman, 53, referring to him as "Norman" while Coleman used a more deferential "vice president" in talking about his opponent.
Republicans banked on Coleman's youth and charisma to overpower Mondale's elder statesman aura and any sympathy vote that would go the Democrats' way following the death of Wellstone, his wife, daughter, three campaign workers and two pilots.
Coleman's post-Wellstone theme tried to make an issue of Mondale's age, repeating, "The future is now." Mondale responded to the age issue with, "I've looked into it and there's not much I can do about it." His campaign tagline was "Serious Experience."
Voter turnout was heavy with each of the candidates forced to wait about 30 minutes before voting.
"I voted for me, and I think Laurie (Coleman's wife) voted for me,'' Coleman quipped. "And if we win by two, we will have put us over the top.''
Vote counting dragged on because the Senate results were cast on supplemental paper ballots that had to be tallied by hand.
The apparent defeat was only the third of Mondale's long political career. In 1980, he was again Jimmy Carter's running mate and the ticket sank amid economic turmoil and the Iran hostage crisis, ushering in Ronald Reagan's presidency. In 1984, he lost his own presidential bid to incumbent Reagan, carrying only Minnesota in the process.