The 18-year-old, who hit the post with a header to create the opening goal, was caught late on the ankle by Matt Lowton and his boss demanded more focus from officials
The Red Devils boss saw two first-half goals from Danny Welbeck and a third from Tom Cleverley push his side to their first Premier League victory in five attempts and end of run of two consecutive defeats.
However, Moyes blasted the home side, whom he felt had targeted Januzaj, claiming officials must do more to protect the teenager after Matt Lowton caught his ankle with his studs.
"I think in every game recently, I don’t know how many tackles have been put in on Januzaj," the Scot told reporters. "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."
But Paul Lambert denied any wrong-doing on the part of his side and believes his players were entitled to go in for the challenges.
"If you look at my team, we’re not a physical side," he said. "We’re a young side where maybe over exuberance gets the better of them. I don’t think anyone will say we’re the most physical side in the world.
"It’s not one of those games where we were over aggressive or anything like that. Yes there were some challenges that people were entitled to go for but I don’t think it was malice.
"What was disappointing was the goals we lost. For the first and second we were actually in possession of the ball and we turned it over, and for the third we’ve got to stop the cross."