Januzaj scored an excellent goal for the champions to double their lead on Saturday at Old Trafford, showing excellent skill to skip past James Collins and place an effort beyond goalkeeper Adrian.
However, the 18-year-old Januzaj was booked for diving late in the first half after going down under pressure from Collins, his second yellow card for simulation this season, having also been cautioned against Sunderland.
However, while Moyes reiterated his stance against diving, after previously speaking out against Young for it, he has defended for Januzaj.
Asked if he supported players diving, Moyes said: "Definitely not. I've had a chance to see it and I think he believes he is going to get sized.
"He has been kicked in every game, upside down. But we will make sure and do everything that we can to make sure it doesn't happen.
"Everybody can see the talent the boy has got. He has got great composure and he is a very good player.
"He is 18 – he has had a lot of games – maybe more than he would have thought. I thought he has warranted his place, though."
Moyes hailed his team for their professional display against West Ham after United won a league match at Old Trafford for the first time in nearly six weeks.
"We are [delighted]. We are pleased," he added. "We played well, we scored three goals and on another day we might have scored more."
Moyes added that striker Welbeck – who went off early in the second half with an injury – was suffering from a knee problem, while he also lauded the efforts of substitute Young.
Moyes said: "It was a magnificent finish. He [Young] got a great goal in midweek and really made sure he put the game to bed with his goal."