The 56-year-old actor has starred alongside the Hollywood icon in six Mission: Impossible movies and admires how the Top Gun star "conducts himself" when he receives attention from the public.
"I mean, he's not able to go anywhere," Pegg told The Sunday Times magazine.
"But when he does, he's very aware of who he is, what it means. So, yes, I do look at how he conducts himself and have realised you just have to chill out. Anybody who gets frustrated or rejects people that come up to them to say nice things is an asshole."
Pegg enjoys being "normal" with the Rain Man actor.
"I've been able to hack my way through all the bizarre mythology that surrounds him - I like being normal with him," The Shaun of the Dead star said.
Meanwhile, Pegg has been open about the fact that he used to drink heavily when depressed and believes he would still be an alcoholic if he wasn't in the spotlight.
"Yes. Fame didn't cause it, it might have exacerbated it at times and thrown it into sharper relief but, no, it was in me before and just happened slightly in public rather than in private."
Pegg explained that he wants to "live a long life" and has got into shape through daily 10km runs and strength workouts.
"Well, after I quit drinking I decided to get into shape. There was something positive about just looking after myself, and I love working out because it gets endorphins flowing and gives me a routine," he said.
"The guys that were 56 when I was a kid seemed like my f***ing grandad, and I just want to live for a long time. Because, you know what? I like life."
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