The Scot admits he is disappointed with the conduct of the Toffees' top scorer, believing his resulting lack of options in attack could weaken their European quest
Fellaini has been handed a three-match ban by the FA for the offence, leaving Moyes' side light in attacking options over the busy Christmas period.
It is a prospect which the Everton boss thinks could potentially damage his side's quest for a spot in Europe next season, and he made no attempt to hide his frustration with the Belgium international.
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“I have spoken to him a few times about it," the Scot told reporters. "I said at the time that I had felt he had let us down and that hasn’t changed.
“We needed him. This is a busy time of the season where you do pick up injuries and suspensions. Things will happen, you may get a sending off — but you can’t do what he has done.
“He knows he has done wrong, 100 per cent. He is a good lad, he is aware that he has got it wrong.”
It has been suggested Fellaini's suspension will leave the Everton attack lacking in creativity, but Moyes insists only time will tell what the precise consequence of his absence will be.
“We’ll find out," he added. "That’s 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.”
The loss of Fellaini will be even more keenly felt during the hectic Christmas period, and Moyes freely admits his priority over the coming weeks is damage limitation.