Fellaini has come in for heavy criticism since following Moyes from Everton to Old Trafford in a big-money summer deal worth in excess of £27million.
The Belgian international has been targeted by fans after a number of uninspiring performances, including United's 1-1 draw at home to Bayern Munich in the first leg of their Champions League quarter-final tie on Tuesday.
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Moyes, however, is sticking by Fellaini and insists he is starting to adjust to life at United.
"I actually thought Marouane Fellaini got better as the game went on," Moyes said, when speaking about Fellaini's performance against Bayern at Old Trafford.
"We needed him, and I thought he played very well. He did well in the Aston Villa game and I think he's getting much closer to scoring goals.
"It's not an easy move, as I can tell you, leaving a club and coming to Manchester United. And for Marouane, I think it's proved equally as difficult, but I have to say I think he's done a lot of good things.
"We bought Marouane not to play every single game in the Premier League.
"He did a great job at West Ham and against Aston Villa. We've had to use him because of what we have available at different times. I think he's improved."