The Ghanaian, who was handed a rare start, spurned a 56th minute penalty to restore parity after Henri Saivet and Mohamed Diame gave the away side a 2-1 lead, Marko Arnautovic having opened the scoring for the Hammers in the sixth minute.
The 28-year-old, however, made amends with a strike 13 minutes later but the effort was still not enough to curtail a reversal at the London Stadium.
“Probably, we hadn’t deserved to get back into the game because in the first half, they had two good chances where they hit the post and the bar, but we needed to get back into it," Moyes said, as reported by his club's official website.
“The crowd had been good to us and stayed behind us and if we’d got the penalty I think it would have changed things.
“We’ve already missed two penalty kicks since I’ve been here and, when you’re in the position we’re in, you’ve just can’t afford to do that and you’ve got to take your chances.”
Saturday's setback is West Ham's fifth defeat in nine games since Moyes replaced Slaven Bilic last month.
“It was just a game full of errors. It was an error from them for the first goal, but certainly from us it was error after error all game and we just couldn’t pull it together,” the manager added.
“We kept at it, huffing and puffing, but never really produced anything of any note in the whole game.
“Individually, we have to take responsibility for some of the things we’ve done. We’ll look at things and see what we could have done better as a team, but we just really messed up for the third goal, we missed a penalty on the day and just didn’t do the jobs well enough.
West Ham currently sit one place above the relegation zone ahead of Tuesday's meeting with Bournemouth.