His loyalty lies not with the country where he was born, Odessky said, but with the country that gave him the opportunity to succeed.
"I think people who live here, American people … they really don't understand where they live," Odessky said. "They live in a beautiful country and when they wake up in the morning, they have to kiss this ground. And when they go to sleep they have to kiss it again." .
(Read more: The 'quiet billionaires' shaping Ukraine's future)
Many of his clients feel the same way.
Over traditional Russian dishes of sour cabbage and potatoes, Steven Mirlas, an IT and pharmaceutical entrepreneur who lives in Brooklyn, explained his position about the Olympics and Russia.
"To be honest with you, I'm not a big fan of the Russians," he said. "We're immigrants from the former Soviet Union, so ... I see the United States going all the way and ... I'm very happy that they are doing very well. All of us who live here are really patriots of the United States. We believe we live in the greatest country in the world, which it is."