The match officials missed the incident as it happened while the players were jostling for a corner in the second half and consequently the Football Association will now review the incident on Monday to decide on the punishment due for the Belgian.
Speaking in his post-match interview, Moyes stated that Fellaini's actions must be accounted for.
"We will take the punishment if it’s given for it [the headbutt], I’ve told him in the dressing room that it’s not acceptable and I won’t accept it as a manager that he does that," he said.
Stoke manager Tony Pulis concurred with Moyes' comments, stating that Fellaini must face punishment as the referee missed the affair.
"I thought the rules were set out in stone. I like Mark Halsey, I think he’s a good referee, I don’t know whether he’s seen it but we’ll find out tonight but if he’s seen it and not acted then you really want to know why hasn’t he acted.
"I don’t think he can hide behind anything and what he’s [Fellaini] done is wrong.
"We get up and get on with it."