Goals from Javier Hernandez and Marko Arnautovic sealed a 2-0 win over Watford at the London Stadium, lifting West Ham up to 12th place.
As quoted by Sports Mole in his post-match press conference, Moyes wants to keep improving despite his admitted surprise at their league position.
He said: "I thought we started really well. We were very wary of Watford after their performance and result against Chelsea. That was a concern. But we nullified them. We have threats in attacking areas - Javier Hernandez, Michail Antonio and Marko Arnautovic - which ultimately hurt them in the end.
"I wasn't so happy with our second half. We didn't win much and I thought Watford were first to most things. But we defended well enough. We still merited it, we stuck at it and got the job done.
"When I took over we were in the relegation zone, I'd have said 'you're kidding' if you said we could get into the top 10 when I took over. It's great credit to the players. We want to keep improving."
West Ham are now level with Saturday's opponents Watford, but they face a tough fixture in a fortnight in the form of a trip to Anfield to face Liverpool.