Animal charity the RSPCA has removed the 27-year-old's two cats as they investigate the incident.
Moyes was criticised for picking Zouma against Watford on Tuesday after the video of the defender emerged.
"There are different views whether he should be available. We decided he should. I stand by that," said Moyes.
Zouma has been fined the maximum amount possible by the Hammers, with the fee being donated to animal welfare charities.
"I don't think a club could have taken action any quicker than they've done at the moment. West Ham have done a really good job," added Moyes.
"I'm not condoning him, his actions were terrible. They were diabolical but we've chosen to play him and we stand by that.
"We will get him some help. We are trying to do as much as we can as a club, as a team, to help him.
"Like people who maybe have drink-driving offences, most of them have to go to classes to learn the reasons and the damage that can be done.
"I think RSPCA are going to provide us some courses for Kurt to understand about animals and how to treat them.
"He's incredibly remorseful. Like everybody else, in life sometimes you need a bit of forgiveness. He's hoping he is forgiven for a bad action."