The Scot was sacked less than a season into a six-year contract after succeeding Sir Alex Ferguson at Old Trafford, with United finishing that 2013-14 campaign outside the European places in seventh.
He then struggled at Spanish side Real Sociedad as well – but saw United make only limited improvements under his successor Van Gaal, finishing fourth and then fifth before the Dutchman gave way to Jose Mourinho this summer.
Moyes maintains he was the right man for the job after Ferguson’s departure, having led Everton from the lower reaches of the Premier League into European contention.
“You don’t get offered those big jobs – Real Madrid, Barcelona, Manchester United – for no reason,” he told several national newspapers.
“I’ve said all along I was unfairly treated there. When you sign a six-year contract and you end up with 10 months … yeah, I believe I was.
“I didn’t win enough football matches but you must say there were mitigating circumstances. And I think you could say there are maybe things which have gone on since then that would actually justify that even more so.
“What my time at Manchester United gave me is an unbelievable idea of what it is at the top. I believe that’s where I can work and that’s where I should be working, and my level is that.”
The experience has not stopped him considering transfer moves for his former United players Marouane Fellaini – who also played under him at Everton – and Adnan Januzaj.
Moyes, appearing before the media for the first time since replacing England boss Sam Allardyce as Sunderland manager, said he was moving quickly to bring reinforcements to the Stadium of Light.
“If any of those good players want to join me I’d be happy to have them,” said Moyes when quizzed about the pair.
“They’re excellent players. We’re interested but I’m sure there’s a load of other clubs that are as well.
“We’ve got offers in for people already. We’re interested in lots of good players.
“But you have to have a realistic view. There’ll be some players we can attract just now and some players we can’t.”
Sunderland have yet to make a single addition to their first-team squad since narrowly avoiding relegation from the Premier League, with departures and injuries leaving them worryingly light on numbers with less than a fortnight to go before the start of the new season.
Moyes thinks that is partially down to the Football Association’s pursuit of Allardyce but vowed to bring with him the acumen he showed at Goodison Park.
His troubled 10-month spell at Old Trafford was scarcely mentioned as the Scot repeatedly drew comparisons with his successful stint on Merseyside.
“The FA had been talking to Sam for three or four weeks. I don’t know if you can really do much business in that period,” he said.
“We’ll get signings in. If you look at the transfers we had at Everton I think we had the best transfer record of any club anywhere in the Premier League. I hope to somehow replicate that in my time at Sunderland.
“Can I do that right away? No. It’s not as easy now as it was before. You’re not going to change it in one transfer window.
“What we want to try and do is get the right players at the right price, like we did in the early days (at Everton). Players who we think can go the journey with us.”
Moyes arrived at the Academy of Light armed with a list of his achievements – a bid, perhaps, to re-establish his credentials.
“I think I’ve got the fourth best winning record in the Premier League of all managers,” he said, referring to number of victories rather than ratio.
“That’s what I want to bring to Sunderland. I need players and I need teams that give me an opportunity to do that.
“The job is to win the games. At the start we may have to win a few ugly but as we go along I hope it will become more exciting.
“This has got to be a building job. Hopefully I’m here for four years and I’ll try and bring a level of stability to the club.
“This reminds me a little bit of Everton when I took over. Everton had been in the bottom six, I think, four out of the five years before I came in.
“In my last eight years I never finished outside the top eight.
“Hopefully we can do a bit of an Everton.”