Despite only being 18-years-old and having played just 11 times in the Premier League, the weekend's yellow card was Januzaj's second from simulation.
However, Moyes was quick to jump to the defence of his playmaker, claiming he has been targeted by some rash tackling early in his career.
Premier League statistics highlight Januzaj as the most fouled, on average per game, player in the top flight, something which Moyes believes referees can do more about.
"I can only say what I see," he said. "In the previous games he has been getting kicked from pillar to post and the referees have been quite happy to let that go.
"They have not been too bothered about doing anything about it. The boy was wrong with what happened on Saturday and we have told him about it.
"But we all make one or two mistakes and the boy will learn as he gets older."
Unhappy with some of the tackling, Moyes admits he would not blame players who dive out of the way to avoid serious injury.
He added: "The thing is, when you are getting kicked all the time and folk are lunging into tackles into you, sometimes you have to jump out of the way or you are going to get hurt.
"That is what I continually say. I just hope it doesn't take a sore one before people start doing something about it."
Almost a decade ago Sir Alex Ferguson was fielding similar questions about diving in regards to Cristiano Ronaldo and Moyes claims protecting Januzaj's fitness must be of paramount importance.
"Some people need to realise this is a young talent," said Moyes. "At the moment they are kicking him but it is right, they also kicked Ronaldo and look at the player he went on to be.
"Adnan will also go on to become a great player in time. At the moment the job is to make sure he is able to play."
Manchester United travel to the KC Stadium on Boxing Day to face Hull, who have conceded just three goals on home turf this season, and Moyes understands it will take something special to penetrate Steve Bruce's fortress.
"It is a great record," said Moyes. "In this league you have either got to score plenty of goals or not concede them, it is one or the other.
"As far as Steve Bruce is concerned, it means he has a good base and his team are hard to beat. It gives him a platform to play off and means he can hope the odd goal wins him matches.
"It will be a tough game that's for sure but we have got ourselves on a winning run and hopefully we can continue that."
Watch Hull City take on Manchester United live on Sky Sports 1HD from 12.30pm on Boxing Day, or for just £4.99 with a NOW TV day pass.