Moyes admitted midfielder Fellaini should have been sent off in the 1-1 draw at Stoke, branding the Belgium international's apparent headbutt on Ryan Shawcross as "not acceptable".
Fellaini is facing the prospect of retrospective action from the Football Association over the incident in the second half.
"We will take the punishment if it is given for it," Moyes said.
"I have told him (Fellaini) in the dressing room that it is not acceptable - I won't accept it as a manager that he does that."
Asked how he might compensate for losing a player as influential as Fellaini to suspension should the 25-year-old be handed a ban by the FA, Moyes said: "There is no absence yet, but he is a really good player and a big part of the team, and that is why I think the biggest disappointment, if anything does happen, is that he will have let the team down."
He added: "I only normally complain if I think we are getting hard done by and I have said a few things about how I think we have been treated by decisions recently.
"So I think if you are going to talk about it with your own team... Today, it should have been a sending-off in the game.
"If the referee (Mark Halsey) had been able to see it, it should have been."
Stoke manager Tony Pulis claimed Fellaini had in fact been guilty of three unpunished offences, and referenced others he felt had been committed by different players against his team this season.
"I'll say this - David Luiz's challenge on Jon Walters (in a 1-0 defeat at Chelsea), Ciaran Clark's challenge on Glenn Whelan last week (in a 0-0 draw at Aston Villa), and then the three incidents today," Pulis said.
"I thought the rules were set out in stone. I like Mark Halsey and I think he's a good referee, but I don't know whether he has seen it.
"If he has seen it and not acted, then you really want to know why he has not acted."
He added: "I don't think you can hide behind anything and what he (Fellaini) has done is wrong."