The midfielder has yet to cement his place in the United side since arriving for £27m from Moyes's former club Everton, whom the Premier League champions face on Wednesday, in the summer.
His manager has admitted that Fellaini has not taken to life with the Red Devils instantly, but is confident that the 26-year-old will prove himself to be a worthwhile signing in the long run.
"He's not had the best of starts but this is a difficult club to join and settle in right away," he told reporters.
"It's a new manager as well, so from that point of view, he can take time to settle in. But he's a good player and has been for a few years at this level, and I have no doubt he'll go on to prove it with this club."
Fellaini, who spent five years under Moyes's management at Goodison Park, is yet to score in his 10 United appearances and was an unused substitute in the 2-2 draw with Tottenham Hotspur on Sunday.