The two players were jostling during a second-half corner when Fellaini lunged at Shawcross before attempting to make a run for the ball. Match officials missed the incident.
Everton manager David Moyes says "I've seen it, it's a terrible thing to do and I expect him to be punished."
The Football Association will review the incident on Monday before deciding whether to charge the Belgium international, who has arguably been Everton's best player this season.
Moyes says "I've told him it's not acceptable and whatever he gets, he and us deserve it."
The match at Britannia Stadium finished 1-1.