Moyes said he thought Januzaj was anticipating a challenge from James Collins when he went down, also highlighting the massive number of tackles the teenager is having to withstand.
And whilst the Scot has spoken out against diving in the past, and has already censured Ashley Young for it this season, he is equally concerned about the rough treatment being meted out to the 18-year-old.
"Adnan is expecting a challenge from Collins," said Moyes.
"We will talk to him about it but you might be picking on the wrong person because if you look at the last two games, he has taken more tackles than any other player.
"I said last week there were a lot of people having a kick at him, because he's very difficult to mark.
"He's elusive the way he moves and it can bring defenders into tackles.
"The referees have to call it right and I just hope he doesn't get a bad one before they do."
Moyes was also concerned at a George McCartney challenge on substitute Javier Hernandez in the second half many observers felt warranted a straight red card rather than the yellow dished out by referee Mike Jones.
"I thought you'd have asked about that one before Januzaj," said Moyes.
"The referee didn't give it so I can only go on what he saw. He saw a bit of simulation in the other one but didn't see that."
Moyes was delighted with the overall performance of his team.
Danny Welbeck scored his first goal at Old Trafford since October 2012 before Januzaj made a mug of Collins to double the advantage prior to the interval.
Ashley Young netted another brilliant effort in the second half so Carlton Cole's consolation did not threaten a fourth successive win, equalling the best run of Moyes' short reign so far.
"The rhythm in attack is beginning to get better," said Moyes.
"We are beginning to create more chances. We had the chances to score maybe four or five but overall we were really pleased with how we played."
West Ham remain outside the relegation zone, but only thanks to the deficiencies of others, and could be in for a very tough season unless boss Sam Allardyce can spark some significant improvement.
"It was the right result," said Allardyce.
"I can't complain about that because our performance in the first half was not good enough.
"We are not in a very good position and we are all concerned with that, owners included.
"You need your best players fit and at the moment we are missing them.
"It's a difficult task for us now and it will be a long haul in terms of digging ourselves out."
Allardyce will hunt for additions in January, as will Moyes, although the United boss is not convinced he will get them.
He said: "We'll look but I wouldn't turn around and say we're massively sure we'll get them because a lot of the players we'd be interested in won't be available in January."