The Doctor Who and Broadchurch actor, 42, who starred in The Politician's Husband on BBC2 this year, said he could not understand why political dramas were not more popular.
The Bathgate-born star said: "It seems there's nothing so compelling as crime drama. It's funny, political dramas aren't so popular as they should be. I enjoy dabbling in that world and The Thick Of It is wonderful.
"But I guess the terrible truth is not enough viewers are interested. They should be. If you don't have an opinion and don't vote you have no right to complain about anything."
Tennant, who is set to star in BBC1 legal thriller The Escape Artist, also admitted he is plagued by self-doubt despite his on-screen success.