Januzaj scored a fine 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.
The Belgian born star is not the first United player to be involved in such controversy, with Ashley Young guilty of similar offences earlier in the season, however Moyes has defended the teenager.
"I think that he is expecting a challenge. If you look at the last two games, he’s taken more tackles than any other player. We’ll talk to him about it but you might be picking on the wrong tackle today," he told reporters.
"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.
“The best thing is just to try and win the next game. There is a long way to go, we’ll just try and keep winning and see where we end up.”
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."
Meanwhile West Ham boss Sam Allardyce admitted his growing frustration with the number of injuries in his squad.
“We’re not in a very good position in the league," he said. "When Downing, Reid, Vaz Te and Carroll are playing we get more quality in the side.
"Not disrespecting anything the players are doing at the moment, everybody wants their best players fit for as long as possible. You need your best players fit for the majority of the season and at the moment we’re missing them.
“If there are any additions we can add in January the chairman has said we can go ahead and do it. It is a difficult task for us now.”