The Belgian attacker has become a marked man in the Premier League this season but has often reacted angrily to the attention he receives from opponents with Moyes urging him to follow in the footsteps of Messi who simply gets on with the game.
"Everybody wants to kick Messi because it is the only way to stop him, but all he ever does is sort of smile, get up and get on with it, and then does it again,” said Moyes.
"So I have told Fellaini he has to copy that. I don't think he'll ever be as good as that, but certainly in his temperament, he should try to be similar to Lionel Messi, who looks as if he just gets on and accepts that people have to try to stop him some way.
"You trust officials and expect them to go about their job the same for everybody. But if you look at Fellaini, you know he has to take as many challenges as anybody.
"He will give as many out, but I don't think he gets protected as well as what there is when he is challenging somebody. It is frustrating, but I've got to say he has got good at it."