Januzaj scored his first Old Trafford goal as West Ham were beaten 3-1 on Saturday, but the winger was shown a yellow card for diving over James Collins' outstretched leg.
He was booked for a similar offence at Sunderland earlier in the season and Moyes - a long-term critic of players who dive - has promised to act despite mounting a defence of his man.
The United manager said: "I saw it, but I believe he thought he was going to be chopped down.
"He's been getting kicked upside down for weeks but we'll be making sure (diving) doesn't creep into his play."
Moyes preferred to focus on the qualities which have already made Januzaj's a fans' favourite in less than half a season as a first-team regular.
"Everyone can see the talent the boy has got," he said. "He scored a really good goal, he's got composure and he's got really good feet and once again he did really well today.
"He's making big steps because he is only 18 and he's had a lot of games but I think he's warranted a place. He's creative and can beat people and we want as many of those players at Manchester United as we can."
It has been a good week for Moyes who saw his team progress into the semi-finals of the Capital One Cup on Wednesday with a 2-0 victory at Stoke City.
And, speaking to Sky Sports after the West Ham game, Moyes argued the home side could have scored more goals.
He said: "We played well today and on another day we might have scored more but overall I am really pleased with how we played.
"I thought we had enough of the ball before the opening goal and it was certainly coming. But, the first one was a really good piece of forward play between Wayne Rooney and Danny Welbeck and it's good to see Danny scoring another goal."
Boy have I criticized Young before and will continue to do so until he performs for the team and not for himself. But that strike yesterday made me lose my breath, take a bow. Yesterday's performance was more like United, has Moyes found his feet? Too soon? Ok then.- utd_till_i_die