The Hammers won 2-1 thanks to Callum Wilson's injury-time goal. Everton also had a penalty shout for hand-ball late on waved away.
Moyes said afterwards: “We’re disappointed we’ve not been able to maintain (our form).
“We’ve conceded a couple of goals today and we did last week, as well. That’s not like us.
“We need to find a way of getting better if we’ve got any chance.”
On the penalty denial, Moyes also said on evertontv: “I think VAR are saying it’s grappling.
“Well, the centre-forward wasn’t grappling. It was the boy marking him. He put his two hands around him and put his hand towards the ball. He reacted and he punched the ball.
“I’m amazed they’ve not given a penalty-kick for it. I think it was VAR who made the decision. I don’t know who was on it today, but they certainly got it wrong, that’s for sure.”
Moyes added: “If anything, we should’ve been the team going on to win 2-1 and not lose 2-1, but it didn’t end up that way.
“I don’t think we deserved to lose, that’s for sure. I thought we played well enough at times of the game.
“We had moments we didn’t do so well, but certainly didn’t deserve to come away with nothing.”