He spoke warmly of the United staff but, perhaps pointedly, not the players.
I remain proud to have led the team to the quarter-finals of this years 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 said.
Moyes was sacked on Tuesday after only 10 months. Newspapers reported on Wednesday that Ferguson had supported the decision to sack Moyes and would play a role in the appointment of the next manager. Moyes said he was and would always be incredibly proud to have been appointed manager of United.
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, he said.
The scale of the managers 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.
United have an urgent need to revamp their ageing squad and are expected to ship out several high-profile players once the season is over.
Moyes said he had already been working on that when the owning Glazer family decided to call time, the manager informed of his dismissal on Tuesday after details had been widely leaked to the media.
We were fully focused and committed to the process of the fundamental rebuilding that is required for the senior squad, he said in his statement.
However, 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.
Moyes said he had seen in his short reign just how special it was to work at Old Trafford and the training ground.