The winger struck twice on his full Premier League debut in victory at Sunderland.
Moyes said: "I've had that experience with Wayne and one or two other players. We'll just make sure he's not treated any different and try not to get the media too hyped up about him. But it's difficult not to talk about a boy when he puts in a performance like that and he scores two goals. But he deserves it. He's a really humble boy and grounded boy. I've not got too many fears about him."
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