The Dutchman believes the Scot's immediate changes "backfired" and likened the 51-year-old's task at Old Trafford to moving from "a yacht to a cruise liner"
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Moyes was sacked on Tuesday morning after just 10 months in charge, while United are already guaranteed to register their lowest ever Premier League finish and have broken a number of unwanted records during the 51-year-old's reign.
Meulensteen, who spent 12 years at United, left the club seven weeks after Moyes' appointment and the Dutchman believes the Scot's decision to make immediate changes "backfired".
"United were a very successful team, with many successful years behind them," Meulensteen told Sirius XM.
"The strategies in place worked. I think David ignored the advice that was given to him by many of the staff in place at the time.
"He opted to put his own plans in place, which he was perfectly entitled to do, but I think it backfired on him.
"It became very evident to me after a few meetings with David Moyes that he wanted to bring in his own people and do it his own way.
"I felt very strongly that things would change dramatically for myself and the position I held so I didn't feel there was a good foundation to carry on, basically."
Meulensteen also feels Moyes failed to judge the scale of the task at United following his 11-year stint in charge of Everton.
"One of the things I did say to him, I tried to warm him: 'Do you realise, after everything at Everton, you're going from a yacht to a cruise liner? That's how big the difference will be'," said Meulensteen.
"It's not just necessarily the work you have to do on the pitch. It's everything that surrounds Manchester United football club, the players, the performances, the pressure, the style, the identity.
"And I think, to be perfectly honest, he underestimated that."