With Wayne Rooney and Robin van Persie struggling with injuries, Januzaj has been thrust into the spotlight to a far greater extent than would be imagined for an 18-year-old.
Moyes has been delighted with the youngster's contribution.
But he does acknowledge such huge responsibility has come rather early.
"We have used Adnan a lot, maybe a little bit more than we would have liked," said Moyes.
"But he has shown he can stand up and can play in the big games. It wouldn't matter what game we played him in.
"He is the future of the club."
As he signed a five-year contract in October, it could be argued Januzaj has achieved his primary objective for the season, namely integrating himself at Old Trafford.
The player's father, Abedin, has always said he wanted Januzaj's club future to be sorted out before he would decide which of the countries he is eligible for he should commit himself to.
Belgium, the country of his birth, have a keen interest in getting an agreement now so Januzaj could represent them in the World Cup.
However, it has been suggested Januzaj would prefer to wait and complete his residency in England before appearing for them.
It seems though, there have been no developments.
"The goal was always to be playing for Manchester United first," said Januzaj's agent Dirk de Vries.
"That was the most important thing as far as the father and the player were concerned.
"At some point a decision will be made but there is no suggestion of there being any change to the situation as yet."
Meanwhile, Moyes feels Mark Hughes is in a similar situation to the one he inherited when he took over as Manchester United manager last summer.
United visit Stoke in the Premier League tomorrow having already beaten the Potteries outfit twice this season.
Like Moyes, Hughes replaced a man who had become a fixture at the club following Tony Pulis' exit after seven seasons.
Unlike the United boss, he has been battling through the last hours of the transfer window to try and strengthen his squad ahead of a fight for survival over the final weeks of the campaign, with Lee Cattermole and Thomas Ince particular targets.
"The one thing Mark has got, as I have, is a solid foundation," said Moyes.
"Tony Pulis did great work but the manager has changed and with change, things becomes different.
"I am sure Mark is having to look at players to see who can go the journey with them and the ones he wants to change around.
"He is not going to be able to do that in one window.
"He will be hoping to get through this period, finish the season as strongly as he can and then see what happens after that."