"I wish all of them well, but particularly the president, the first lady and their daughters.
"This is a time of great challenges for America, and I pray that the president will be successful in guiding our nation."
Governor Romney thanked his running mate Paul Ryan, saying he hoped he would continue to use "his intellect and his hard work and his commitment to principle" for the good of the nation.
After paying tribute to his wife Ann and his family for their support, he went on to thank his campaign team for their "extraordinary effort, not just for me but for the country that we love".
Governor Romney then addressed the challenges America now faces, saying: "The nation, as you know, is at a critical point. At a time like this we can't risk partisan bickering and political posturing.
"Our leaders have to reach across the aisle to do the people's work and we citizens also have to rise to the occasion."
He called on teachers and professors, pastors and priests to inspire children and enforce the "enduring principles" on which American society was built -- "honesty, charity, integrity and family" - and asked employers and job creators to continue to invest and hire staff.
He also appealed to those across the political divide to "put the people before the politics".
Governor Romney said: "I believe in America. I believe in the people of America, and I ran for office because I am concerned about America.
"This election is over, but our principles endure. I believe that the principles upon which this nation are the only sure guide to a resurgent economy and to a new greatness."
Telling his supporters he and Mr Ryan had "left everything on the field" in their campaign efforts, he said: "I so wish that I had been able to fulfil your hopes to lead the country in a different direction, but the nation chose another leader, and so Ann and I join with you to earnestly pray for him and for this great nation.
"Thank you and God bless America."