The 18-year-old was booked for simulation in the first half of United’s breezy 3-1 win over West Ham United on Saturday after going down in the general vicinity of James Collins, but also scored a superb goal and might have earned a penalty.
However, while Moyes accepted Januzaj’s yellow card was justified, he was more concerned that referee Michael Jones only handed out a booking to West Ham defender George McCartney following a horrendous stamp on the ankle of Javier Hernandez late in the contest.
“He (Jones) saw a bit of simulation in another one, but didn’t see that,” said Moyes.
“I think Adnan was expecting a challenge from (James) Collins, but if you look at the last two games, the amount of tackles he has had to take, he has taken more tackles than any other player.
“So we’ll talk to him about it, but you (journalists) might be picking on the wrong person today.
“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, it can bring defenders into tackles.
“But it’s the referees who have to call it right and I just hope he doesn’t get a bad one before they get it right.”
Danny Welbeck and substitute Ashley Young were also on the mark for United before West Ham pulled back a consolation goal through substitute Carlton Cole.
The game witnessed Welbeck’s first goal at Old Trafford in 14 months and saw United’s recent improved form continue. They have now won four games in 11 days across three competitions, with only one goal conceded.
It also ended a run of two consecutive home league defeats for the champions and Moyes said: “We’ve had a couple of really good victories since then and today (Saturday) was another good win, so I’m really pleased with that.
“I’m pleased for the players. I think they’ve earned it and played well, and on another day we might have scored more and probably should have. I’m really pleased in how they’re performing.
“The rhythm in attack is beginning to get better, we’re beginning to create more chances. The first goal was great combination between Wayne (Rooney) and Danny and it was good for Danny to get himself a goal.
“It keeps his goals going. We want him to become a goalscorer as well as a good player and it was good he got that finish.”
Welbeck, scorer of the opening goal, came off with a knee complaint, which is a concern for Moyes given the absence for the next three weeks of Robin van Persie with a thigh injury.
The England forward will undergo tests this week to assess the damage.
Meanwhile, West Ham manager Sam Allardyce conceded that injuries and basic mistakes have left his team embroiled in a long, hard relegation campaign.
“We’re not in a very good position in the league,” he said.
“We’re obviously all concerned about that, the owners included. It’s a difficult task — 14 points after 17 games — and it’s going to be one of those long hauls in terms of getting us out of that position.”