The London Stadium was blighted by some troubling fan protests during the club's defeat to Burnley in March, but since then the Hammers' support has moved to get behind the side, most notably in their last home victory against Southampton.
Heading into a crucial final few games of the season, Moyes has insisted that he expects the club's fans to carry on showing their collective support ahead of a vital period.
"The West Ham supporters have sensed we need them and we have sensed their support and because of that we've done well," Moyes told reporters ahead of the club's game with struggling Stoke City on Monday night.
"I thought the support against Southampton was fantastic and I thought the way they paid tribute to Ray Wilkins at Chelsea did the club proud. I've got no doubts they'll do the club proud again on Monday night.
"In my first evening game, against Leicester City, it was a Friday and the atmosphere was brilliant. Let's hope for more of it and if the players produce the form they did in the last game, I think we'll give them something to shout about as well."
The Hammers currently find themselves in 14th place in the standings, six points above the bottom three.