Said Benrahma's late strike - his first goal for the club on his 31st appearance - rescued a point after what looked to be a late winner from Danny Welbeck at The Amex on Saturday.
Before the game, the Hammers knew that three wins from their final three fixtures would take them into the Europa League at the very least, but Saturday's draw meant that Tottenham's subsequent win over Wolves saw the north Londoners climb above West Ham into sixth place thanks to their superior goal difference.
The result means that West Ham's fate is no longer solely in their own hands. To finish inside the Europa League places they must now rely on others - mainly Spurs - to fall short across their remaining games while taking maximum points themselves.
A seventh-placed finish would take West Ham into the new Europa Conference League, Uefa's third-tier European tournament.
But David Moyes’ side are not giving up on the top six yet.
"This is our dream and we want to do the maximum, to be there at the end of the league," said Soucek. "Two games to go and we need six points.
"We’ve talked about wanting to play Champions League or Europa League, it is still alive. We want to do the maximum to finish sixth or higher."
Manager Moyes bemoaned a lack of sharp decision making in the final third as West Ham spurned chance after chance on the south coast, and Soucek says the squad are well aware of the problem.
"It is not good enough for us," he said. "We came here and wanted to win because we want to be in the Europa League or more. We created many chances but we need to score more.
"We said in the changing room that we need to score, the last few games we’ve been losing and it’s hard to change to a winning game. In the next game we need to be prepared for the first chance and score."