Januzaj has been one of the enduring shining lights in a difficult transitional season at Old Trafford.
The 18-year-old has started United's last three Barclays Premier League games and chose Saturday's 3-1 win over West Ham to score his first goal on home soil.
What a beauty it was too as Januzaj left James Collins looking a mug as he stepped inside the experienced Hammers defender, taking him out of the play completely, before drilling home an impressive shot.
Little wonder the United fans have taken him to their hearts.
Moyes is mindful of expecting too much too soon from the youngster. However, that should not be confused with letting Januzaj have an easy time.
"We are always going to be hard on Adnan," said Moyes.
"We will push him all the time to get more off him. He is an exceptional talent and, for an 18-year-old, he is doing remarkably well.
"We have to be mindful of his age but we are really pleased with how he is doing."
Given his public stance on the curse of diving, Moyes will be uncomfortable about the fact that Januzaj has now been booked for it twice this term.
His fall at the weekend was dramatic as Collins pulled out of an intended challenge, leaving the youngster flying through the air over nothing.
Yet Moyes is getting irritated by the treatment being meted out to Januzaj, who had a reasonable penalty claim turned down when he was levered out of the way by Mark Noble.
"We will have a word with him because his job is to make sure he does things right," said Moyes.
"But I am concerned about how many tackles he is having to take in every game.
"He is getting tackled and kicked more than anybody.
"He thought Collins was going to have a scythe at him and he was going to ride it. It looked a bit worse than it was."
United have been down this road before with Cristiano Ronaldo and could do worse than get Ashley Young to have a word with his team-mate given the England star has had his own issues with diving in the past.
Over the past couple of games though, Young has been attempting to stay on his feet, and bouncing back up immediately if he has hit the deck.
In addition, the former Aston Villa man has scored a couple of wonder goals, following up his first for 19 months at Stoke on Wednesday by curling home a delightful effort from Wayne Rooney's lay-off to wrap up a fourth win on the trot for United.
"It is like when buses come along, you get two at once," said Young.
"To get two in a week is fantastic. I am not too sure what the secret is. Shooting I guess."
Young needs to rediscover the form he showed in 2011 to become a regular feature in Moyes' new-look United, and give him a chance of making the England World Cup squad.
More immediately, he will be one of the players United need to spark at Hull on Boxing Day as they hunt a fifth successive win.
It is a measure of the difficulties United have had this season that they will celebrate Christmas Day in their lowest position of the entire Premier League era.
Their troubles do seem to be easing though, which cannot be said of West Ham, who were awful, remain perilously close to the drop zone and face Arsenal at Upton Park next.
"We are not concerned because there is a lot of quality in our dressing room," said long-serving defender James Tomkins.
"That is the most important thing. We are experienced in this league and have experienced problems before. Hopefully we can get out of it."