The 18-year-old winger came in for some rought treatment against Aston Villa on Sunday.
Moyes claims officials must do more to protect Januzaj.
“I think in every game recently, I don’t know how many tackles have been put in on Januzaj,” Moyes said. “That’s what I’ve been annoyed with; it’s the fourth official and the referees.
“Before you know it, the boy will get a sore one because he’s definitely not being protected by the officials and it’s terrible what they’re allowing to go on at the moment.
“It’s not necessarily the same player. I think they were taking turns to see who will kick him next. I think it’s something that the referees are going to have to think about.
“It’s up to the referees. They’re given that job; they’re paid to referee the games. You would hope that they would recognize that. He’ll just get up and he’ll walk away from it.”