United fell behind at the Stadium of Light in the fifth minute when Craig Gardner fired home.
But on his first Premier League start, the 18-year-old Januzaj powered in Patrice Evra’s cut-back before sealing the win with a stunning volley in a six-minute spell after half-time.
“Since pre-season we’ve noticed a big improvement in him – he looked a proper player,” Carrick told Sky Sports.
“I was telling him at half-time to get in the box a little more because there were chances for him. And they were two great finishes that have won us the game.
“He’s got so much ability and great attitude. He can be anything he wants to be – he’s that good and he’s got that chance.
“But it’s just a start and I’m sure he’s not going to get carried away by it. We’ve got a lot to thank him for today.”
He added: “From within we never really believed we were in a bad position. We controlled the game, kept believing and we knew we had a chance to win the game in the second half.
“Credit to the boys for sticking together and believing.”
The win, just their third of the season, hoists United up to ninth place in the Premier League table.
But Carrick insists that David Moyes’ men have not been lacking confidence and belief, despite a stuttering start to their title defence.
“We’ve been successful here as a team,” he continued. “The manager’s changed but the character and the desire is still there.
“As a team, you have good and bad days – and we’ve had too many bad days in recent weeks.
“But that’s part of football. It’s a test for us. We relish the challenge and we’re not in bad shape now.”
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