Fellaini was booed off by fans when he was replaced during Everton's shock FA Cup quarter-final defeat last weekend, with supporters unhappy with the Belgian's attitude.
An appearance at an official Everton store earlier this week was postponed and Moyes accepts Fellaini's stock may have fallen with the fans.
However, Moyes is prepared to give the 25-year-old a chance to make amends when Everton face Premier League champions Manchester City at Goodison Park on Saturday.
"His reaction wasn't right, it wasn't the correct one and I have told him that," said the Everton manager.
"He knows that he should have played much better, and yes, he may have some making up to do with the fans, but I won't have any trouble picking him.
"I'll play Marouane against Man City as I have to give us the best chance of winning. That means picking our best players and giving them a chance to make amends.
"Don't forget the good stuff he's done. For the most part he's been outstanding and made a huge contribution.
"Most of the lads had a disappointing day, even if he found it tougher than most.
"He may not be firing as he might, but he's still been influential for us. He is the only player I'm talking about, but there were eight others we could be talking about."