The Scot, who signed Fellaini from Everton after being appointed as Sir Alex Ferguson's successor, was dismissed after less than a year in charge of the side.
The Belgian told MUTV: "It was a hard week for me [last week] because I was close with the manager. I was sad, but that's football. Results are the most important thing in football so the club decided to make the choice.
"Now we have a new manager and we are looking forward. We have three more games left in the season and we want to finish strong."