Despite being identified by United legend Alex Ferguson as the ideal man to replace him, Moyes endured a woeful campaign as the club finished seventh and missed out on European qualification.
United reached the quarter-finals of the UEFA Champions League before defeat to Bayern Munich, but crashed out of the FA Cup in the third round to Swansea City.
Moyes was in the Old Trafford hotseat for less than 12 months, despite agreeing a six-year contract after his departure from Everton, and the 51-year-old is now ready for another managerial role.
"I'm ready to return," he told the BBC.
"I have enjoyed the time off but I have got to wait on the right job and make sure it's one that I want.
"I'm really ambitious. I would never have left Everton for anybody but an ambitious football club. And I thought Manchester United would have given me that opportunity.
"It didn't materialise that way, so I am hoping that the next club I join gives me the chance to build a team, because I think that is what I am good at.
"It doesn't need to be a club that is in European football but I've got to say the time I had in the Champions League last year - getting to the quarter-final in the Champions League wasn't a bad feat.
"I really enjoyed it - embraced it, actually loved the Champions League nights, and we did well."
He added: "I got the job and I expected it to be a six-year plan. I signed a six-year contract... [I am] disappointed it didn't go to plan.
"I expected to be given an opportunity to fulfil that and it wasn't what was expected.
"It was really difficult when I lost the job initially because I didn't really see it coming, even though I had been losing games.
"I knew that it could be difficult but I joined a club that I felt stood behind their managers, made sure they supported them in difficult times. And, you know, Sir Alex had difficult times when he first took over.
"And I do understand that the landscape has changed a little bit in football, but I think that United always stood for the right things and I expected them to do what was right with me."
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