"It's just one of those things, you miss out on more than you get," he told The Washington Examiner.
He said he's been working on independent projects, but was most recently turned down for a role on one of television's hottest shows, the Examiner reported Thursday.
"Actually I was up for a part on 'Homeland,' " Thompson said. "But I didn't get it."
He said he can't choose a favorite career between politics and acting because "it's hard to pick among your children," but can point to his role in "The Hunt for Red October" as his favorite acting job.
"First of all I played an admiral, which, I've gotta say, is kind of in my wheelhouse. I have never been an admiral, but you know, most actors haven't," Thompson said. "Plus it was just a great movie and it was probably the last Cold War movie where the Soviet Union was the bad guy."
Thompson is a former Republican U.S. senator from Tennessee.