The actor also told The Times that he understood the distinction between fiction and reality when he first watched the programme.
Tennant said: "I remember, after seeing Jon Pertwee turn into Tom Baker in Doctor Who, having a conversation with my parents at a very young age about actors and what they did.
"I remember getting the distinction between a character and an actor, as they explained it. I understood what fiction was very clearly."
He added: "I always feel uneasy when people talk about children not understanding the difference between fantasy and reality.
"I can only have been three, and was just enthralled. But I was quite clear that I didn't want to be a Time Lord - I wanted to be the person who played a Time Lord."
David Tennant will leave Doctor Who after this year's specials and be replaced by Matt Smith for the fifth series of the show.