The England attacker is on-loan at Everton from Manchester City this season.
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Barry, who also played for both clubs, told Sky Sports: “It is a move Jack needed. I think Jack needed regular football. He needed the love from his manager to go out there, and go ‘show me what you can do’.
"Not too many instructions. Just go and be Jack Grealish. And I feel he’ll get that at Everton with David Moyes.
“Having played with the Everton fans, they’ll back him. They’ll get right behind him. And if Jack does what he does, he will have a great season. He’s already started well. I’m sure he can improve on that as well.”