Fellaini endured a mixed first season at Old Trafford, but has earned praise after impressing in the club's last two outings.
Moyes signed the Belgian midfielder for £28m in September 2013 after the pair worked together at Everton, and the Scot has every confidence that Fellaini can continue to get his United career back on track.
"Marouane should have been given time too, because he's now proving what I always believed: that he can be an important player for United," Moyes told the Daily Mail.
"I've watched him in the last two games and he has been first class. He's had an influence on the games, which is what you look to your bigger players to do. And I think he's played an important part in helping United gain some momentum going into the Manchester derby.
"There were times last season when things were tough, when we spoke. But I told him then that he would become a top United player if he continued to work hard."
Fellaini has made four appearances for United so far this season.