"While I may have had a -- suffered a personal setback last night, I couldn't be more optimistic about the future of this country," he said at a press conference Wednesday.
Cantor recognized the sergeant-at-arms and the Capitol Police, particularly those who served on protection details, along with the staffers who "are the backbone of this institution."
Cantor repeatedly told reporters he would "leave the political analysis to y'all," and refused to speculate on why he lost his election.
During the run-up to Tuesday's primary, Cantor sent out mailers on immigration taking a hard stance against amnesty, while playing the issue somewhat softer while on the Hill. On Wednesday, he denied changing his position on immigration, saying he believed the current system is broken and in need of reform.
"I don't believe in this 'my way or the highway' approach that the president has taken, and I've continued to take that position," he said. "I've always said that there should be and is common ground, if we just allow ourselves to work together."
After a meeting of the Republican caucus at the Capitol, Cantor announced he would be stepping down as leader on July 31st, and a special election will be held next Thursday to chose his replacement.
Campaigning for Cantor's job has already begun: Rep. Kevin McCarthy, R-Calif., the majority whip, began lining up support from committee chairs Wednesday. Perhaps most importantly, he has the support of Cantor, who threw his weight behind McCarthy at the press conference.
"I think he'd make an outstanding majority leader," Cantor said. "I will be backing him with my full support."
As members streamed out of the press conference, most walked past the gathered reporters and cameras, putting up a hand to indicate their unwillingness to speak or a shake of the head. Those who did elaborate or offered passing remarks noted how "gracious" Cantor was or how how "great" he had been has majority leader.
Members said House Speaker John Boehner sounded like he was choking up while he spoke about the history he shared with his top lieutenant.
"This is a speech I never expected to give," he said. "I want to start by offering a heartfelt thanks to Eric and his staff for their service to our conference, our institution and our country."
Quoting Winston Churchill, Boehner advised Cantor to have 'the courage to continue."
"He was held in high regard as a leader, so we're feeling the pain," said Rep. John Kline, R-Minn., his eyes red.
"A lot of tears. I've never seen such grace in all of my life," said Rep. Renee Ellmers, R-N.C., fighting back tears. "He is doing the right thing for the conference."
"He wants to keep us all united and I just think he is doing a fabulous job and he is going to do well into the future and we all stand behind him."