Moyes feels that Fellaini can learn a lot from Barcelona star Messi's temperament.
"You trust officials, and you expect them to go about their job the same for everybody," Moyes told ESPN. "But if you look at Fellaini, he has to take as many challenges as anybody. He'll give as many out, but I don't think he gets protected as well as what it is when he's challenging somebody.
"It is frustrating. But he's good at dealing with it. I keep saying to him: Look at Lionel Messi. He gets kicked every week. Everyone wants to kick him because it's the only way to stop him. But all he ever does is smile, get up and get on with it.
"So I've told him he has to copy that. I don't think he'll ever be as good as that, but certainly he should try to be similar in temperament to Lionel Messi. He just accepts it and gets on with it. He accepts that people are going to try to stop him some way and moves on."
Everton host Oldham Athletic in an FA Cup fifth-round replay on Tuesday.