West Ham were reduced to 10 men when Masuaku was sent off soon after the break for spitting and the defender apologised for his conduct on Sunday.
"I want to say sorry for my actions yesterday," he said on Twitter. "It was in the heat of the moment and out of character for me but I know it was totally unacceptable and I will learn from the first red card of my career."
Masuaku is facing the prospect of a six-game ban and Moyes said that the club would also take disciplinary action against him.
"It was despicable," Moyes said. "I've not seen it from him. We like him, he's a really good boy around the club... it is out of character."
"He will deserve everything he gets and he'll get something he deserves from us. It's unacceptable."
West Ham, who are 11th in the Premier League, take on 13th-placed Crystal Palace on Tuesday.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Amlan Chakraborty and Clare Fallon)
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