Januzaj struck a brace after Sunderland had gone into halftime 1-0 up.
Moyes said: "He's a very, very good player. But we will do everything we possibly can to keep his feet on the ground. We played him in the reserves at Bolton last Monday.
"That's what we will do at the club. He's a very humble boy, works hard, so we will do everything we possibly can to keep a level on it, but we know we have got a really exciting talent there.
"All young boys want to play for Manchester United. I don't know a better place for them to have the work, the coaching, a club that promotes young players - and I'd like to say a manager who promotes young players as well.
"If I was a dad of a young boy who was good enough, I would be saying, 'I think there's a chance of you getting in the Manchester United team because they push you forward and they promote their young players'.
"That's part of my remit and I was more than happy to play Adnan today."
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