The 50-year-old released a statement via the League Managers Association in which he spoke of his gratitude to Sir Alex Ferguson, the fans and the staff at Old Trafford
There was no mention of the United players, who have kept tight-lipped since Moyes left the club
Even those players normally so active on Twitter have remained silent on the matter
Moyes was sacked as manager by the club on Tuesday, and former United captain Roy Keane said some of the players "should be ashamed of themselves".
Ryan Giggs has been appointed interim manager and was assisted at training on Wednesday morning by former team-mates Paul Scholes, Phil Neville and Nicky Butt.
Moyes said he felt proud to have taken the team to the Champions League quarter-finals but that he understood fans' frustrations at the overall results.
He said in a statement: "During this period of transition, performances and results have not been what Manchester United and its fans are used to or expect, and I both understand and share their frustration.
"I remain proud to have led the team to the quarter-finals of this year's Champions League and I remain grateful to Sir Alex Ferguson for believing in my ability and giving me the chance to manage Manchester United."
He added: "To have been appointed as manager of Manchester United, one of the biggest football clubs in the world, was and remains something of which I will always be incredibly proud.
"Taking charge after such a long period of continuous stability and success at the club was inevitably going to be a significant challenge, but it was one which I relished and never had a second thought about taking on.
"The scale of the manager's job at United is immense, but I have never stepped away from hard work and the same applies to my coaching staff.
"I thank them for their dedication and loyalty throughout the last season.
"We were fully focused and committed to the process of the fundamental rebuilding that is required for the senior squad
This had to be achieved whilst delivering positive results in the Barclays Premier League and the Champions League.
"In my short time at the club I have learnt what special places Old Trafford and Carrington are
I would like to thank the United staff for making me feel so welcome and part of the United family from my first day
And of course thank you to those fans who have supported me throughout the season
I wish you and the club all the best for the future."
Source : PA
Source: PA