The £38m arrival from Ajax scored on his first start for the Hammers as they began their Europa League campaign with a win against Serbian side Backa Topola on Thursday evening.
Much is expected of the Ghanian international, who represents a major coup for the east London club following summer links with a move to Chelsea and Arsenal.
Still, Moyes is prepared to be cautious when it comes to bedding in Kudus, particularly with his West Ham side having started the season so strongly as it is.
“We’re getting used to us and we’re still getting used to him, as we’ve said about a lot of our new players who have come to the Premier League,” he said.
“We’re going to give Mo the opportunity to settle in, but he made a good contribution on Thursday night.”
Jarrod Bowen is a doubt for the trip to Liverpool on Sunday, with the England international suffering from illness.