"A year ago today, we were getting ready for a big celebration," he said. "It didn't work out exactly as we had planned."
He said the campaign left him more in love with America and more inspired with its uniqueness than ever.
"If you get the chance to run for president, do it," said Romney, who shared the stage with Costas before this same group in 2001, when Romney headed Salt Lake City's Olympic organizing committee. "I am more in love with America and more concerned with our future. America's role is essential. I think we are on a road that is making us a little weaker. We need to have a stronger path."
That was about as political as it got.
Under questioning from Costas, Romney said he had no interest in becoming the commissioner of a major sports league such as Major League Baseball.
He also said that stadiums and sports venues should be built by owners and not the government, though it was appropriate for the public to build roads and infrastructure to support those venues.
"The Olympics are different," Romney said. "That is America putting on an event for the world to attend. People ask why we spend $2, $3 and $4 billion and not give to the poor instead. Every now and then, it's a good thing for America to host the world and have people to be here serving the world. Every 10 or 20 years, we need to invest to bring the world here."
Costas asked Romney if the International Olympic Committee should steer clear of countries with objectionable policies.
Romney said yes, using Germany hosting the Games in the 1930s when Hitler came to power as an example. But he said the Olympics should not be boycotted nor should they be seen as a political event.
Costas said that the Beijing Games in China were used to promote the country with an over-the-top Opening Ceremony he doubts will ever be equaled because there was no budget.
"I am sure that people were watching in the U.S. feeling admiration and awe and a little bit of trepidation. If they can do this, what else can they do?" said the sportscaster.
"They have designs to lead the world," said Romney of China. "What you saw at the Olympic Opening Ceremony was a prelude to march on the world stage economically."
On another topic, the failed Republican presidential candidate said he thought it would be a mistake for schools to eliminate sports and the arts from their curriculums when they are looking for ways to cut budgets. He said sports provide the place where kids learn life's lessons far beyond the history books.
"For young people, a sports experience is essential to growth and development," he said. "As a country, we will suffer if we as a nation cut out sports. The same with arts."
Costas, who will be the Olympics' studio host for the 10th time in Sochi, Russia, next year, countered that college sports were experiencing major problems with athletics often not coexisting well with academics.
"It's not something that coexists with the educational experience," said the Emmy-winning sportscaster. "There is an arms race to finish first to justify revenues. Schools are recruiting students who are not capable of graduating who have criminal records and behavior problems. That corrupts the entire experience. No one should get an athletic scholarship who could not plausibly get in without an athletic skill."
Asked what he remembered about Salt Lake City's Olympics, Costas said he recalled the athletes bringing in the Sept. 11, 2001, American flag in the Opening Ceremony, the 1980 U.S. Olympic hockey team lighting the caldron, the anxiety and determination to hold a successful Games after the Sept. 11 terrorist attacks and the judging scandal involving the pairs figure-skating competition as the most memorable moments.
Costas also called the 1998 NBA Finals game when Michael Jordan hit the winning shot to beat the Utah Jazz.
"That was the end of one of the epic careers in American sport," he said. "No athlete had a better closing act. … That might have been the final image of Michael Jordan in the NBA. And they were playing a worthy opponent in Karl Malone, John Stockton and Jerry Sloan. To quote the late Jim McKay, that was the thrill of victory and agony of defeat. All the pieces were in place."
Romney's final words for the group involved the role sport plays in the world.
"Sport plays a much bigger role than just entertaining us," he said. "It lifts us. It is a major part of the American and world experience."
The TEAMS Conference & Expo that runs through Thursday aims to help athletes of all ability levels and ages compete in venues big and small. The event, sponsored by SportsTravel Magazine, is the world's largest gathering of sports-events organizers.
"The TEAMS Conference & Expo is committed to providing a platform for the leading thinkers and practitioners in the sports travel industry," said Timothy Schneider, publisher of SportsTravel Magazine. "The importance of long-term relationships is one of the key themes of TEAMS '13."