Moyes was hand-picked by Sir Alex Ferguson to replace him as manager in May 2013, and the Scot signed a six-year contract. But the current West Ham United boss was dismissed after only 10 months in charge, which left Fellaini feeling distraught.
The Belgian was Moyes' first signing at the club after arriving on a deadline-day deal in August 2013 for £27.5million.
"He brought me to England, then signed me for Manchester United, one of the biggest clubs in the world. I can never say anything bad about him.
"I've said this since the beginning; if you give Moyes time, he will make a team. I've watched West Ham a few times this season. They've become a side that's difficult to beat.
"If I'm honest, I cried when I found out Moyes lost his job at Manchester United. I thought he was going to stay for a long time.
"It was a sad day. I went to his office to say goodbye, before he said bye to everyone. I told him, 'Good luck'. But it was a difficult time for me.
"Moyes is a top man, he has a big heart. That's why maybe he didn't succeed at Manchester United, because he's too nice.
Moyes subsequently had largely unsuccessful stints in charge at Real Sociedad and Sunderland, before his first spell at West Ham in the second half of the 2017/18 season.
His six-month contract at the London Stadium was not renewed, but he returned to the club in December 2019 and will be in the dugout for his 1,000th game as a manager for the Hammers' Europa League match against Genk on Thursday.
Meanwhile, Fellaini stayed at Old Trafford until February 2019 when he joined Chinese Super League team Shandong Luneng in 2019. He made 177 appearances across all competitions for the Red Devils, scoring 22 goals and registering 12 assists.
The midfielder also won the FA Cup, League Cup, Europa League and the Community Shield during his time in Manchester.