The Toffees boss has encouraged the Belgian midfielder to keep his cool like Lionel Messi when faced by opponents who attempt to unsettle him and incite an angry reaction.
The Belgian is set to take his place in the Toffees' lineup for their trip to St James' Park after completing a three-match ban he served for headbutting Stoke's Ryan Shawcross in the 1-1 draw between the two sides at the Britannia Stadium.
Moyes was naturally disappointed to lose the talismanic midfielder to suspension, and he believes Fellaini must change his attitude and have it in line with that of Barcelona star Lionel Messi if he is to avoid similar punishment in the future.
"The best person you have to look at is Lionel Messi. Every person targets him, they'll do everything," Moyes. told The Daily Star. "But all he ever does is get up and get on with it. That's the sign of a top player. It says to people, 'Whatever you do, it doesn't affect me.' I tell Felli that you just have to get on with it. If I was playing against Felli, I'd try and wind him up."
The 25-year-old Fellaini has been in excellent form for the Merseysiders this term, scoring eight times in 19 games, but he was quick to admit that his decision to strike Shawcross was regretable.
"My headbutt on Ryan Shawcross was frustration, as he had spent the entire game pulling and pushing me, but I shouldn't have butted him," Fellaini said. "I exploded and I am sorry for doing so."