The 18-year-old Belgian winger, who had earlier been booked for diving, dragged a misfiring United back into the game with a calmly-taken 55th-minute equaliser and then smashed a dipping volley past keeper Keiren Westwood to win the match just six minutes later.
On an afternoon when United were far from their best, they needed something special to get back into the game after falling behind to Craig Gardner's fifth-minute opener.
And Carrick, who played alongside Januzaj, believes he is good enough to 'be anything he wants to be'.
"He's done it on the big stage and he's made a big improvement and he's taken his chance in pre-season and he took it on his first start, two great finishes. He's won us the game," Carrick told Sky Sports.
"He's got a great attitude. He can be anything he wants to be, he's that good. I'm sure he's not going to get carried away with himself. The second (goal) was a terrific volley."
Carrick also denied that United let their heads drop after they went a goal down.
"We never really believed we were in a bad position," he said.
"We controlled the game and gave them a couple of chances early on. Our backs were against the wall but we knew we had a chance to win the game. Credit to the boys for believing and we stuck together.
"The character and the desire is still there. As a team we have good and bad days and we've had some bad days over the last few weeks. We relished the challenge of the game."