The movie depicts Roosevelt's relationship with his mistress Margaret Suckley (Laura Linney) against the background of World War II.
Discussing the film with The Boston Globe, the actor revealed that he was disappointed that FDR cheated on his wife Eleanor Roosevelt.
"When I first read the script, there was a little bit of, 'Ohhh [sigh]. Really?'" Murray recalled.
He added: "I'm pretty sure [adultery is] a mortal sin. I have that in my DNA, painted on the walls of my ribs.
"But I've been more influenced by everything else that he did, by everything else he achieved, by the selflessness of the rest of his life."
Murray went on to say that it was very difficult to reconcile Roosevelt's personal failings with his massive impact on US history with the New Deal, which helped America emerge from the Great Depression.
"I always have difficulty saying, 'It's okay, he can do that 'cause he did a great job with everything else'," he explained. "That's sort of obviously true but it doesn't come out of your mouth very easily.
"Hey, this man devoted his life to public service; he had a dalliance with another woman, or maybe a couple of other women.
"Is it one of these cognitive things where you go, 'Let's look at both sides of the ledger'? I never felt comfortable with that. That's sort of not the way I operate."
Murray recently cited Hyde Park on Hudson as one of the most challenging projects of his career, specifically because he was playing a historical figure.
Hyde Park on Hudson opens on Friday (December 7) in the US and on February 1, 2013 in the UK.
Watch a trailer for the movie below: