Fellaini laments Moyes United exit
The Scot was fired just 10 months into a six-year contract after it became mathematically impossible for the faltering English champions to qualify for next season's Champions League.
Belgium international midfielder Fellaini worked with Moyes at Everton for five years and was his first major signing at Old Trafford.
"It was a hard week for me (last week) because I was close with the manager," Fellaini told MUTV.
"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."
Ryan Giggs has been put in caretaker charge until the end of the season.
The Welshman has added fellow 'Class of '92' members Paul Scholes and Nicky Butt to his coaching staff.
Fellaini has been impressed with how the new management trio and Phil Neville, who stayed on as coach despite being initially brought in by Moyes, have responded since Moyes's exit.
"When they came in the first thing I saw was that the players respect the manager and I think that's important," the 26-year-old Fellaini said.
"They were big players before and they know the club and the biggest manager (Sir Alex) Ferguson."
Fellaini did not make the bench for Giggs's first game in charge -- a 4-0 win over Norwich -- but hopes to be included in the Welshman's matchday squad for Saturday's home game against Sunderland.
"I respect the choice of the manager," Fellaini said when asked about being dropped.
"I've worked hard in the last few days to get into the squad, I did last week as well."