The Hammers claimed a 1-0 victory over Tottenham on Sunday, taking them to fourth on the table with 17 points.
Moyes told Sky Sports: "I thought the game was close. We played slightly different today in that it was good to see that we've won the game without having as much of the ball. In Premier League games you have to find different ways to win it.
"Tottenham had a bit of possession but overall we were really resilient. The players stuck at it. The players were fantastic. We have lost goals in the last minute in games after Europe so we've got over that today. The West Ham fans have got a good team that work hard for them - everybody was really good in the stadium.
Asked about a potential top-four push, Moyes added: "It's where I want us to be, it's where I expect us to be. There have been a couple of games we've missed out on when we've played well enough. Today we didn't have as much of the ball and play quite as well but winning games is important on the back of two other wins. It's been a good week for us."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!