The narrow victories of former Navy Secretary James Webb in Virginia and state Sen. Jon Tester in Montana mean Democrats secured 51 Senate seats and the majority in the upcoming 110th Congress.
Democrats also took control of the House in Tuesday's elections, giving them the majority in both chambers for the first time since 1994.
Webb declared himself the winner early Wednesday, saying, "The votes are in, and we won. This is a great moment for all of us."
Allen said Thursday that the people of Virginia had spoken "and I respect their decision." He promised to work with Webb on his transition into office.
Allen, a former governor of Virginia, was favored to retain his seat early in the race, but several developments on the campaign trail helped set up Webb's win.
During a rally in southwest Virginia in August, Allen called an Indian American Democratic volunteer "macaca," for which he later apologized. Then, former acquaintances accused Allen of using a derogatory term for blacks years ago.
He addressed these charges by saying, "I made a mistake, careless words. I've apologized for it, and it's been discussed quite much. And then you have these baseless allegations who do not depict who I am, how I was raised, or what I believe in."
Webb also was targeted for comments and positions he took in the past, including criticizing the admission of women to the Naval Academy in an article he wrote 27 years ago. A campaign ad for Allen featured female academy graduates slamming Webb.
After the bitter contest, Webb secured the seat with a margin of about 7,200 votes out of 2.37 million cast. Allen, who could have requested a recount since the margin was less than 1 percent, chose not to take that path after initial canvassing of the results failed to show much change in the results, reported the Associated Press.
In Montana, meanwhile, Burns received 194,904 votes, or 48.3 percent, to Tester's 198,302 votes, or 49.1 percent.
The three-term senator conceded defeat to Tester on Thursday, congratulating him by telephone.
"I stand ready to help as Montana transitions to a new United States senator," Burns said in a statement to the AP. "We fought the good fight and we came up just a bit short. We've had a good 18 years and I am proud of my record."
"This was a hard fought campaign and I think that Montana is glad it is in their rear view mirror and Jon Tester is ready to move forward," said Tester spokesman Matt McKenna.
