Januzaj was then given his marching orders in the 89th minute after his second caution for a late foul on Tottenham sub Ben Davies – right in front of the home dugout.
Moyes said: “I was disappointed with Adnan, but I was also disappointed with the referee.
“It should have been a free-kick to us on the edge of the box – you could see he was having his jersey pulled.
“He didn't give it and Adnan should not have spoken back to the referee.
“The second yellow could have been a yellow, could be.
“I've seen that one back on television and it looks worse on the television than it does stood pitchside.
“It didn't look an awful lot at pitchside.
“I think [the first yellow] he had a case for his disapproval."