The Belgian international starts a three-match ban on Saturday for head-butting Stoke City's Ryan Shawcross during last week's 1-1 draw at the Britannia Stadium.
Fellaini has been a talismanic presence in midfield as Everton have enjoyed a strong first half of the season, and Moyes fears the club could suffer from his absence.
"I'm not sure [how we will cope]," he said. "We will find out. That is why it was a big miss to lose him. We will have to try and find solutions, but we don't have loads of solutions to fix it. People shouldn't be surprised if we aren't able to solve it."
Moyes revealed he has spoken to Fellaini about his conduct before and has left the 25-year-old in no doubt that he has let the club down with his latest misdemeanour.
"You can't do what he has done," he added. "He knows he has done wrong - 100 per cent.
"I have spoken to him a few times about it. I said at the time that I felt he had let us down and that hasn't changed. He let a lot of people down."
Moyes added: "We needed him. This is a busy time where you pick up injuries and suspensions. Things will happen - you may get a sending off.
"He is a good boy, a good lad. [But] he is aware that he has got it wrong."
Moyes is also sweating over the availability of another Belgian, winger Kevin Mirallas.
The 25-year-old has travelled to Germany for a consultation on a recurring hamstring problem and the Everton boss admits he is concerned about his £6m signing's long-term fitness.
"I am worried, yes, especially when you are a quick, fleet-footed player like he is," he said.
"What we are trying to do is find a way of getting people back quicker, but sometimes with these injuries, you have to give them a bit of time and TLC."
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