Moyes, who was sacked by Real Sociedad last season, recently took charge of the Black Cats following Sam Allardyce's elevation to the England hotseat.
The Scot impressed with modest resources in an 11-year spell with Everton, thrice winning the LMA manager of the year award.
"I've said all along that I was (unfairly treated). When you sign a six-year contract and you end up there ten months, yeah, I believe I was," said the 53-year-old.
"But that is life in football. Ultimately the key is to win football matches. I didn't win enough football matches.
"You must say there were mitigating circumstances. And I think you could say there are maybe things that have gone on since then, that would actually justify that even more so."
Moyes, however, can draw positives from his time at Old Trafford.
"It gave me an unbelievable idea of what it is at the top," he added.
"I believe that's where I can work and that’s where I should be working, and my level is that, because that is what I saw in the time I was there.
"You don't get offered those jobs, you don't get offered big jobs, if you've not done something. You don't get offered the Real Madrid job, the Barcelona job, the Manchester United job, if you've not had something to suggest that there's a reason for that job.
"Yeah I am better [as a manager]. I have had several opportunities, big ones, but timing is so positive. The timing for this job at Sunderland was right. It feels good to me."