"I would expect us to get the punishment, we'll accept whatever punishment is given out for it," Moyes told Sky Sports News after the 1-1 draw at Stoke that left Everton fourth in the Premier League.
"I've told him (Fellaini) in the dressing-room it's not acceptable and whatever he's handed out, he and us deserve it."
Belgian international Fellaini was seen to butt the Stoke captain as they jostled for position at a corner taken by the visitors.
Stoke manager Tony Pulis said he was disappointed the incident was not spotted, while expressing support for referee Mark Halsey.
"If people are not seeing them as red cards, then for goodness sake send a memo around and let us know," he told Sky.
"I've got a lot of respect for Mark...he's been a good referee and I can't tell whether he's seen it or not....if you look at the angles and if he has seen it, again you've got to ask why hasn't he given it?." (Reporting by Alan Baldwin, editing by Ed Osmond)