The club parted company with Moyes earlier this week, and Meulensteen, who left Old Trafford shortly after the Scot's arrival, believes that the former Everton manager made mistakes as he looked to bring in his own staff last summer.
"David ignored the solid advice given to him by many of the staff in place at the time and opted to put his own plans in place, which he's entitled to do but it backfired on him a little bit," the Dutchman, who worked with Sir Alex Ferguson for over six years, told Sirius XM
"Don't forget that David Moyes was a respected manager over 11 years at Everton, but I tried to warn him: 'You do realise that, with all respect to Everton, you're going from a yacht to a cruise liner, and that's how big the difference will be?'
"It's everything that surrounds the club – the players, the pressure, the performances. I think he's underestimated that and unfortunately it's cost him his position."
Louis van Gaal is the current favourite to replace Moyes.