Fellaini was brought to Manchester United by Moyes in the summer of 2013 having worked together at Everton.
But Fellaini struggled to find his place under Moyes and bore the brunt of much criticism from fans in two seasons under Louis van Gaal.
However, under Jose Mourinho the Belgian’s toiling United career has been revived and he has been a key component in their strong start to this season.
Fellaini will miss tomorrow’s clash with Liverpool due to a knee injury.
And Moyes believes his former player doesn’t deserve the criticism he gets, instead hailing him for his one major asset.
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He told BBC Radio Five Live: “He’s never going to be Paul Scholes.
“But he was there to do certain jobs and I think the job he’s doing really well for them.
“I think a lot of people disliked his look and the way he was and thought Manchester United were going to play it long.
“But I think Manchester United are crossing the ball and Fellaini is heading it in the net.
He’s a really good runner which people don’t give him credit for.
“Maybe doesn’t have great high intensity speed but he can cover the ground.
“He puts in as much work as anybody and I’ve said this a couple times, I would argue he’s probably got the best chest control in the world. He’s that good.”