There has been much said about Januzaj's potential for some time and the 18-year-old had a true breakthrough moment on Saturday, scoring twice - one of his goals a superb volley - in United's 2-1 Barclays Premier League win at Sunderland, where he was making his first senior start.
Since then, there has been considerable focus on the Belgium-born player's future, both at club and international level.
Discussions about a contract extension at United, where Januzaj's current deal runs out at the end of this season, have been ongoing since April, although so far there has been no resolution and reports have suggested Barcelona are monitoring the situation.
In terms of representing a national team, Januzaj's complicated background means he is eligible for various countries aside from the one he was born in - he would also be available for England once he has fulfilled FIFA's eligibility requirements - and it has emerged that he does not yet want to decide which to choose.
Carrick has no doubt there is a lot swirling around Januzaj, but is confident conditions are right for him to cope.
The 32-year-old England international told the Manchester Evening News: "It is a lot for a young lad to take to come in like that. The attention he is going to get now will be a lot.
"He is young, he is going to learn along the way and learn fast. I am sure he will be fine.
"Young lads can come in and change. Their life can change overnight and the expectations and pressures change. There are more responsibilities.
"But he is at the right place and he has a good attitude. He is going to stay on the right lines.
"I and the other experienced players are there to set an example and do the right things."
Carrick has emphasised that the very fact United boss David Moyes opted to give Januzaj his full debut meant the rest of the team had no qualms about his readiness for it, even before he netted the second-half brace at the Stadium of Light that steered the Red Devils to their come-from-behind victory.
"You don't want to heap too much praise on him and put pressure on him because he is so young," Carrick said.
"He will probably have good days and he will have not so good days because he is learning the game.
"But at Sunderland he was top drawer. He carried on what he has been doing in training since we got back from pre-season.
"He is good enough. He may be aged 18 but he's not a kid as a player. He is a top player. He is in the team so he is one of us. It doesn't really matter how old you are or how many games you have played.
"The boss picked him so we trust him. There are bits of advice and bits of help that people like myself can pass on. I told him at half-time at Sunderland to get in the box a bit more - so that helped, didn't it!
"In terms of debuts, he has scored two and we have won 2-1 so what can you say about that?
"In some ways he won us the game. His performance was good. He has everything sat there for him to prosper and fulfil his potential.
"He is at the right club. He has the right players around him who are willing to help him and obviously the right manager. He has the ability. As long as he keeps along the right lines and does the right things he has got a great chance of having one of the best careers."
In a recent interview with his club's official matchday programme, United Review, Januzaj spoke about the guidance he is receiving from the likes of Red Devils veterans Patrice Evra and Ryan Giggs.
Januzaj said: "Everyone gives me advice. That's the great thing here.
"People want you to do well and want to help you develop your game. I speak a lot with Patrice and Giggsy. They have great experience, they're big players at the club and have gone through everything I'm going through. Their advice is important.
"If I play on the left, Patrice is just behind so he helps me, and I'm playing in a similar position to Giggsy. I ask him questions all the time as he's been a top, top player for so long. He's a good teacher."
And on the step up he is making to senior first-team football with United, he added: "Everything is quicker. The games are quicker, you have to think faster and play quicker. I'm training with great players almost every day so I do what they tell me but at the same time I want to bring my own qualities too. That's important. You have to do both.
"The technical qualities (of the likes of Robin van Persie, Shinji Kagawa and Wayne Rooney) are brilliant, so just playing alongside them raises your standards. You learn little things like when to speed up play, when to pass, when to hold the ball, all those things... by watching experienced players it just becomes natural."