Ashcroft also rejected the possibility of a challenge to the election, saying he will not take part in any legal action and will discourage others from doing so.
Even so, his colleague Missouri Republican Sen. Christopher Bond has scheduled a press conference for Thursday to ask for a federal investigation into possible voter fraud in St. Louis.
Some Republicans had argued that at the time of the election, Carnahan was not as the U.S. Constitution requires a Missouri inhabitant, because he was dead.
"I don't think my election hinged on voter fraud in the city," Ashcroft said Wednesday. "I lost this race because I didn't get as many votes as my opponent did."
"I hope the outcome of this election is a comfort to Mrs. Carnahan," Ashcroft said in an emotional speech while surrounded by family and two dozen supporters at his suburban St. Louis headquarters.
Mel Carnahan whose named remained on the ballot after being killed in a plane crash on the way to a campaign rally three weeks ago outpolled Ashcroft by more than 48,000 votes out of 2.36 million cast Tuesday.
Never before in U.S. history has anyone posthumously won election to the Senate, though voters on at least three occasions sent deceased candidates to the House.
"Missouri is a compassionate state and, I think, in a very special way, they have demonstrated their compassion," Ashcroft said.
Before the election, Roger Wilson, the new Democratic governor, said that if Carnahan won, he would appoint his 66-year-old widow, Jean Carnahan, to the Senate. She would take on the position after Ashcroft's term ends Jan. 3, and would serve until the next general election, in 2002.
Ashcroft, a former two-term governor, state attorney general and auditor, said he plans to go back to his farm near Springfield after his term ends.
"I look forward to spending time with my wife, Janet," Ashcroft, 58, said, breaking off to fight back tears as his wife laid her head on his shoulder. He said he does not want to think about whether he will seek the same seat in 2002 or run for any other office.
Political observers applauded Ashcroft's speech.
"He's a smart man and a smart politician, and he did everything perfectly in terms of doing what he should have done, being gracious, being sensitive and not closing a single door," said Ken Warren, a Saint Louis University political science professor.
After the plane crash, Ashcroft took an eight-day hiatus from campaigning, which he said hurt him in the polls. If Ashcroft is known as the first Senate candidate ever to lose to a dead person, Warren said, it won't be a negative association.
"Ashcroft had an impossible job," he said. "The whole situation developd very late in the campaign, where the bounce Carnahan got from his tragic death did not dissipate in time for Ashcroft to rebound himself from having to stand on the sidelines while Carnahan was praised."
Mrs. Carnahan conducted a low-key but effective effort consisting mainly of one news conference, one TV commercial and a single interview from the family home.
Early Wednesday, she spoke to hundreds of St. Louis-area supporters from her home in Rolla.
"We remain heirs of a legacy, bearers of a dream," Mrs. Carnahan said. "On this night, I pledge to you rather, let us pledge to each other we will never let the fire go out. God bless you always."