Barry struggled when coming on in last week's derby defeat to Liverpool. The striker has also been booed by Everton fans in recent games after some social media controversy.
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Moyes said: "You can come in and it doesn't happen.
“He came on in a difficult game, at a difficult time in the game. He was up against two big centre-halves and it was probably a tough gig for him at the time.”
On Barry's progress overall, Moyes added: “He's done a lot of good things for us. We're just saying we want more, we're looking for more.”