The Hammers led through a Tomas Soucek header but had a second goal disallowed for offside against Michail Antonio following a goalmouth scramble.
After a lengthy review VAR Jarred Gillett decided the ball had brushed Antonio’s ankle on the goal-line after Craig Dawson bundled it goalwards via the legs of Brighton defender Shane Duffy.
Hammers boss Moyes said: “I didn’t think we played well but we made enough chances to probably nick the game, but a draw was a fair result.
“Obviously it was a big call for VAR which you would probably expect me not to agree with, but I’ve got real reasons not to agree with it.
“It’s nearly impossible to rule that goal out. The ref couldn’t do much, he didn’t see it. The only people who can make the call is the VAR.
“Whoever the VAR has to decide why we can chalk that off. I hope someone comes out and tells us. For me the last touch came off Shane Duffy’s legs.
“I think it’s so hard to call that not a goal. You have to have something much clearer to identify why that goal can’t stand.
“I’m hoping to be showed a real reason why it wasn’t given. And the time it took suggests it was a difficult call.”
Jarrod Bowen and Pablo Fornals also missed presentable chances to put West Ham clear, before toothless Brighton equalised from nowhere thanks to a spectacular overhead kick from Neal Maupay.
It means West Ham have still yet to beat Brighton in the Premier League, after falling short yet again at the ninth attempt.
“I think they are a good team,” added Moyes. “I don’t think I was here for all those nine games. But they have a real style and make it difficult for you. It looked like we were going to win the game and we probably should have done.
Brighton had been booed by some of their supporters after the goalless draw against Leeds at the weekend, with Maupay among the players missing chances.
Seagulls boss Graham Potter said: “We suffered early on tonight in terms of the scoreline which made us feel a bit vulnerable, but I thought we performed well.
“We kept pushing in the second half, we probably rode our luck with the goal they had disallowed, but I felt we deserved something from the game.
“Neal had a difficult game against Leeds, even though his performance was good. If you miss a chance and it’s 0-0 the environment is tough.
“But he was always going to stay on today and it’s really good for him to get the goal. It shows how you can go from villain to hero.”
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