Moyes annoyed that West Ham only sprang to life after going behind
Neal Maupay's 53rd-minute strike secured victory for Everton and consigned West Ham to a fifth league defeat of the season, leaving the London club stuck in the relegation zone at 18th.
"We didn't play well. I've got to say, I don't think Everton played well either," Moyes told reporters.
"Did we deserve to win? No. Did we deserve to lose? Probably."
West Ham showed more urgency after Maupay's goal, striking the woodwork through substitute Said Benrahma, but Moyes said he was "really annoyed" they were unable to raise their game sooner.
"It showed me that they had more to give but really, they stepped up a little bit after that," Moyes said.
"Obviously, I understand Everton probably got the goal and probably felt that they needed to try and protect it. They made it look as if we were playing a bit better at that period, but I genuinely didn't think there was an awful lot in the game."
West Ham, who have just one win from seven league games, next host 17th-placed Wolverhampton Wanderers on October 1.