Flanked by wife Cindy and running-mate Sarah Palin, McCain spoke to supporters outside the Arizona Biltmore Hotel shortly after 9 p.m. Tuesday, saying the "American people have spoken and they have spoken clearly."
He conceded the contest as polls closed on the West Coast, adding a string of states to Obama's electoral vote tally and sealing the Illinois senator's victory.
McCain stressed the historic nature of the election, noting that an invitation to Booker T. Washington to dine at the White House by Theodore Roosevelt had been viewed as an insult in some quarters.
"Senator Obama has achieved a great thing for himself and for his country," McCain said.
Although McCain had criticized Obama during the hard-fought campaign as too inexperienced to be president, the Arizona senator said that "in a contest as long and as difficult as this campaign has been, his success alone commands my respect for his ability and perseverance.
"But that he managed to do so by inspiring the hopes of so many millions of Americans who had once wrongly believed that they had little at stake or little influence in the election of an American president is something I deeply admire and commend him for achieving."
McCain told his supporters that it was natural "to feel some disappointment. Though we fell short, the failure is mine, not yours."
McCain had been all but counted out of the contest for the GOP nomination in the summer of 2007, when his campaign was all but broke, and his comeback was a remarkable political feat.
"I don't know what more we could have done to win this election," McCain said. "I'll leave that to others to determine. ... I won't spend a moment in the future regretting what might have been."
McCain also praised Palin, his surprise choice for vice president. The Alaska governor excited the GOP base, especially evangelical voters, but critics dismissed her political resume as brief and light on substance.
Palin is "one of the best campaigners I have ever seen, and an impressive new voice in our party for reform and the principles that have always been our greatest strength," McCain said, adding that she and her family showed "courage and grace" in the "rough and tumble of a presidential campaign."