Cottagers boss Scott Parker was not best pleased after the match, having seen his team fail to rescue a point having conceded a Tomas Soucek strike in the 91st minute.
"I'm disappointed and angry," Parker told Match of the Day. "You can't take penalties like that and he knows that. He's a young player and he's learning."
"A tough call on Fulham for our goal because the offside rule is not a good rule. I would claim offside for that, but we get a goal from it," said West Ham boss David Moyes.
"The boy has made a mistake. Ade is the first to understand that. When you're young and you're learning you have to learn quick. He is disappointed and rightly so. This is part and parcel of football, of growing as players and as a team. We'll get around him now."
"None of us really know the offside rule now," said Fulham boss Scott Parker. "We've got VAR, every gadget and gimmick and there are so many things to look at nobody knows.
"He's (Haller) interfering with play, my defender can't leave it."