Januzaj was repeatedly fouled during Sunday's 3-0 Barclays Premier League win over Aston Villa but only one challenge - a late one from Matthew Lowton - was punished with a yellow card. The 18 year-old was replaced by Ashley Young shortly afterwards, which later prompted a question about his welfare during the manager's post-match press conference.
"I don't know how many tackles there have been on Januzaj in the last two or three games," said Moyes.
"That's why I've been annoyed with the referees and the fourth officials. Before you know it the boy will get a sore one because he's definitely not getting protected by the officials. It's terrible what they [opposition players] are allowed to do to him at the moment because this boy's an incredible talent.
"Lowton was booked but I think there were that many tackles on him from different players. I think it's something the referees are going to have to think about. They [opposition players] are queuing up to kick him."
When asked if opposition managers should stamp out such tactics, Moyes responded: "No, I think it's for the referees - that's their job."
While concerned about the issue, the United boss is content with the way Januzaj seems to be handling it.