Belgian midfielder Fellaini has been criticised for responding to rough treatment from opposing players this season, but Moyes believes that Messi provides a prime example of how to remain calm under pressure.
"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 I've got to say he's got good at it," Moyes told reporters.
"I keep saying to him, 'Look at Lionel Messi, he gets kicked every week'. Everybody wants to kick him because that's the only way to stop him, but all he ever does is smile and get up and get on with it again, and does it again.
"So I've told him to copy that. I don't think he'll ever be as good as that, but certainly in his temperament. He should try to have a similar temperament to Lionel Messi, who looks as if he just gets on [and] accepts that people are going to have to try and stop him some way, and moves on."
Fellaini received a three-match ban earlier this season for striking Stoke City defender Ryan Shawcross.