Pablo Sarabia put Wolves ahead from the penalty spot in the first half, but a spot kick from Lucas Paqueta and a James Ward-Prowse effort direct from a corner gave West Ham all three points at Molineux.
However, the end result could have changed in the ninth minute of added-on time, Max Kilman powering a header into the bottom corner after meeting a corner.
A draw would have been a fair result after a game in which both sides had dominant periods, yet VAR and the referee ruled that an offside should be given courtesy of Takanda Chiwera standing in the eyeline of goalkeeper Lukasz Fabianski.
Although Chiwera was in an offside position, Fabianski would not have saved Kilman's clinical finish, the referee and technology each ruling that it was irrelevant in this instance.
What did O'Neil have to say?
After the game, O'Neil revealed that he failed to get a sufficient explanation from referee Tony Harrington, admittedly through his own anger at the decision, but he criticised the lack of common sense that was applied to the situation.
Speaking to Match Of The Day, O'Neil said: "Terrible, terrible, terrible decision. I can't understand it at all. I've spoken to David [Moyes] and to be fair he said the same. It's never, ever, ever offside. Fabianski the same, he didn't think it was offside.
"Crazy really that a Premier League referee can stand in front of the screen, having been sent to it, and get it so badly wrong.
"Obviously he's stood in an offside position but the reason it's not offside is that he's not impacted Fabianski being able to dive or move, he's not impacted his line of vision - if you watch the side-on footage Fabianski can clearly see the ball over Tawanda's head, so I don't know how he can be interfering.
"Fabianski is getting nowhere near that header, no matter whether there is no one there or someone there. It's a really, really bad decision and I don't understand how he reaches it.
"If your knowledge of the game is really, really bad, you can come to that conclusion but other than that I have no explanation for it - and I haven't had an explanation from them, and it won't help us."
David Moyes later insisted that the call made by the officials was correct, although accepted that he could see why O'Neil did not agree with the decision.
What now for Wolves?
Wolves now have a welcome week off of action ahead of squaring off against Nottingham Forest at the City Ground on April 13.
O'Neil's side will head into that contest sitting in 11th position in the Premier League standings, rather than within three points of seventh place had Kilman's goal been allowed to stand.