The Hammers were well organised all night and took the lead through a fantastic 30-yard drive from Pedro Obiang in the 70th minute.
Heung-Min Son responded in emphatic fashion with a spectacular strike himself, and Moyes told Ian Abrahams after the game he was content with his side’s performance.
“It was a good point for us,” he said.
“After what we had to do a couple of days ago and play again against a team such as Tottenham, I thought we done a really good job.
“We didn’t have many shots but the one we did have was really good.”
Ahead of a more favourable run of fixtures, the Scotsman admitted his side needed to start beating the teams around them.
“So you’ve got to say that we are doing one part right, we’d like to do the other side of it much better obviously.
“I’m the coach and I have to try and find a way of getting results with the players that are available.”