He has been a long-term critic of United's decision to replace Sir Alex Ferguson with Moyes.
Verheijen told the Mirror: "You really wonder if the people who are responsible at Man United are actually doing their homework.
"I don't think it is so much the problem and responsibility of David Moyes.
"But if the people at United had done their homework they would never have appointed David Moyes, they would have appointed someone else.
"When you are managing Man United you need different tactical qualities to when you are an underdog like Everton.
"It has to do with tactical flexibility."
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