The result at the London Stadium moved West Ham level on points with 11th-placed Watford and five points clear of the dropzone, prompting Moyes to laud the quick turnaround since his November appointment.
"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," the Scot told reporters after the game.
"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."
Up next for West Ham in the Premier League is a trip to Anfield to face Liverpool on February 24.