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 donít know how many tackles have been put in on Januzaj," Moyes said. "Thatís what Iíve been annoyed with; itís the fourth official and the referees.
"Before you know it, the boy will get a sore one because heís definitely not being protected by the officials and itís terrible what theyíre allowing to go on at the moment.
"Itís not necessarily the same player. I think they were taking turns to see who will kick him next. I think itís something that the referees are going to have to think about.
"Itís up to the referees. Theyíre given that job; theyíre paid to referee the games. You would hope that they would recognize that. Heíll just get up and heíll walk away from it."