Goals from Mark Noble and Zavon Hines either side of an Ashley Young leveller saw the Hammers win their first game since the opening day of the season and Villa were reduced to 10 men when Beye was dismissed for a second yellow card.
"I don't want to talk about the decisions," said O'Neill. "It is a pointless exercise. Anybody who has access to a TV monitor can make their own minds up. I have not spoken to the referee.
"I am disappointed to have lost. I think we did enough to get something out of the game. We were in the ascendancy in the first half and their goalkeeper made some good saves.
"We looked a very good threat and thought we would go on to win it. You can lose a goal at any stage but it is disappointing to lose at that stage. We looked tired in the last 15 minutes but it is not an excuse."