The Scot said he had learned some "invaluable lessons" during his time at the club.
Moyes, who took over from Sir Alex Ferguson, was sacked in April when he was just 10 months into a six-year contract.
The 51-year-old said he had had some "very good" job offers since then, but may choose to take a break from working in football.
He told the Sunday Post: " I really enjoyed my time at Manchester United. It taught me some invaluable lessons. I'm sure I will benefit from the whole experience.
"I believe I'll be a much wiser and more knowledgeable coach and manager from the short period I had at Old Trafford."
He told the paper he was " tempted by one or two" of the offers he had had since leaving United
"However I may still choose to have a break and enjoy watching and observing football throughout the world," he added.
"But what I do know for sure is that I have moved on."
Moyes said he believed he would be given more time to implement a revamp at the club and said that players, including Wayne Rooney and Darren Fletcher, had contacted him with messages of support after he left.
He also said: "I believe I had nothing but support from Sir Alex during my short period as manager.
"When I succeeded him he advised me of some changes that had to be made. I took his advice on board and started to implement the changes and modernise certain aspects.
"I also became aware of other changes that were necessary and put plans in place. It was never going to all come together in a few weeks or months."
He added: " It was unfortunate I wasn't given more time to succeed."
- Sports & Recreation
- Sir Alex Ferguson
- Manchester United