The Scot endured a torrid 10-month spell in charge at Old Trafford, after being handpicked by compatriot Alex Ferguson as his successor following 27 trophy-laden years.
United surrendered the Premier League crown to local rivals Manchester City with a whimper, and failed to qualify for European football following a seventh-place finish in the Premier League.
However, Moyes is of the opinion that he could have reversed United's fortunes had he been afforded more time to put his stamp on the squad.
"I never had the chance to thank the Manchester United supporters for the backing they gave me during my time as manager. I wish them every success in the future." Moyes wrote in The Sunday Times.
"They now appreciate, I am sure, that things are changing at their club and it could well be that gone are the days of long-term planning. They were fully aware of the task I had. It was unfortunate I wasn't given more time to succeed."
Despite having been dismissed less than 12 months into his six-year deal, Moyes insists he has moved on and is now pondering his next move.
He added: "Since leaving, I have received some very good offers and am tempted by one or two of them.
"I have not closed the door on anything and am open-minded about my next step in management, and whether it will be in the UK or abroad.
"Another possibility is that I may choose to have a break and enjoy watching and observing football throughout the world. What I do know for sure is that I have moved on."
Moyes also believes he retained the support of Ferguson until the end of his tenure, and stated he attempted to follow his predecessor's advice as best he could.
"I have spoken to Sir Alex Ferguson on several occasions and we met recently at a dinner in London," Moyes explained. "I believe I had nothing but support from him.
"He advised me of some changes that had to be made. I took his advice and started to implement the necessary changes. I became aware of other changes that had to be made and put plans in place."
