Retiring United boss Sir Alex Ferguson was renowned for dishing out what became known as the "hairdryer treatment" but Fellaini - who has played under Moyes for four years - knows all too well how tough the Scot can be after he was banned for headbutting Stoke's Ryan Shawcross.
"He is a decent man, a great manager, but believe me he can be tough. If you want to win something, to create a good team you have to be hard sometimes with the players - football is like this," he told the Mirror. "He can be scary.
"I remember when I was banned after the Stoke game, he gave everyone the day off - everyone: The players, the entire staff - but I came to the training camp to do a training session with him.
"It was just me and him, and it is not easy to go into the camp to face him like that.
"I understood, because I knew I had made a mistake, but you know it's not easy when you know you have let him down. Just going in there knowing you have to look him in the eye was hard!
"He put me through a tough session... it was a full-on session, running, shooting, passing, everything and very intense, and afterwards I was upset.
"I said afterwards, 'Arggh, this is bad', but I am happy when he looked after me, so I understand."