Brighton broke the deadlock with just six minutes remaining courtesy of Danny Welbeck’s 50th Premier League goal and his sixth of the season for Albion.
The England international calmly lifted the ball over Hammers goalkeeper Lukasz Fabianski after being slipped in by substitute Percy Tau.
The lead was short-lived as West Ham substitute Said Benrahma swiftly levelled with his first goal for the club.
"It feels like two points dropped," said Welbeck who is out of contract this summer. "We just switched off and it is not good enough, we need to be better in these situations and as a group improve on that to get to the next level.
"I am pleased with the goal. With injuries and that sort of stuff I would have hit that mark [50 Premier League goals] a bit earlier. There is so much more to come."
On survival being confirmed by Fulham's loss earlier this week, Welbeck added: "It is kind of disappointing, we would have liked to have done it ourselves. With the squad we have we shouldn't be thinking of relegation, we should be looking further up the table.
"As a group we have to gather together, analyse the games and the performances. I think there is a lot more we can do."
The point from the 1-1 draw means the Hammers are five points behind fourth-placed Chelsea with only two matches to play.
West Ham midfielder Tomas Soucek said: "We really wanted to win because we wanted to be in the Europa League or more. It’s still our dream. Two games to go and we need six points.
"We created many chances and you need to score. We started losing [recently] and it’s hard to change to winning games.
"When I came here [last season] I immediately thought of relegation but we won this fight and this season we said we wanted to play higher and it is still alive."