The emergence of the 19-year-old has been one of the few positive points of a below-par season for United, with the reigning Premier League champions sitting sixth in the table and facing a 2-0 deficit ahead of the second leg of their Champions League last-16 tie with Olympiakos.
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"Everyone knew we had a special talent on our hands, but the real test comes when you play at Old Trafford," Neville told United's official website.
"So that was the question back in pre-season: has he got the temperament to play for Manchester United at Old Trafford?
"Well, I think he's answered that. You have to have the courage, the belief, the confidence, the determination to play for Manchester United - those characteristics are key to a player's success here and Adnan is no different.
"It's still early doors for him, though, and I think we've treated him right. We've played him in games and we've also rested him in others and given him a bit of a breather.
"We have to make sure that in two or three years he's still improving and reaching the levels we hope he can reach. That's our job as coaches."
Belgian-born Januzaj - who joined United from Anderlecht in 2011 - has made 26 appearances in all competitions this term, and put pen to paper on a new five-year contract in October.