The Belgian-born youngster has been subjected to roughhouse tactics from top-flight defenders, most recently riding a number of tough challenges during Saturday's 3-1 win over West Ham at Old Trafford.
However, having been consistently fouled, Januzaj went to ground in the second half without contact from James Collins, who had shaped to make a challenge, prompting referee Michael Jones to produce a yellow card for simulation.
Speaking at a press conference on Monday, Moyes said: "What I have seen is that in the previous games he has been getting kicked from pillar to post. The referees have been quite happy to let that go. They have not been too bothered about it.
"The boy was wrong with what happened on Saturday. We have told him. He will improve because he is young. When you are getting kicked all the time and folk are lunging into tackles, sometimes you have to jump out of the way or you are going to get hurt. I just hope it doesn't take a sore one before people start doing something about it."
Moyes compared the treatment Januzaj must expect as similar to that faced by Cristiano Ronaldo in his younger years at Old Trafford. He overcame and utilised that negative attention to make himself stronger, physically and mentally.
"Some people need to realise this is a young talent. [Players] kicked Ronaldo and look at the player he went on to be. They will do it to Adnan and he will go on to become a great player in time. At the moment the job is to make sure he is able to play because he is getting the opportunity and he is getting kicked from every angle. Yes, he has made one or two mistakes but the boy will learn as he gets older."