West Ham boss Avram Grant said his team need seven points from their remaining three games to avoid relegation from the Premier League.
The Hammers lost 2-1 at Manchester City on Sunday to leave them bottom of the table and three points from safety.
Their next two games are against Blackburn and Wigan - two of their relegation rivals - before they host Sunderland on the final day.
"Our target is to take seven points. We will try to take all nine," said Grant.
West Ham have not picked up a point from their last five games, a run which has left them rock bottom with 32 points from 35 games and trailing 17th-placed Blackpool by three points.
And on Sunday they initially appeared to be in danger of of losing by a heavy margin as City ran riot in going 2-0 up inside 20 minutes.
Midfielder Nigel de Jong lashed in a 20-yard drive to give the hosts the lead and they doubled it when Pablo Zabaleta's cross-shot was prodded in off the bar by visiting defender Lars Jacobsen.
Demba Ba pulled one back for West Ham to set up a tense final hour, but fourth-placed City held on for the win.
Despite the defeat, Grant felt his side gave a good account of themselves.
"At 2-0 they were on top of us, and then our reaction was very good," Grant told Sky Sports. "I thought we showed a lot of character today. The second half was good.
"Now we play against a team that are in our area [16th-placed Blackburn next Saturday], so we have to win this game.
"I thought that other teams around us would take more points in the last two games, so the gap stays three points."
Meanwhile for City, the win increased their chances of securing their pre-season aim of securing Champions League football for next season.
They now have a seven-point cushion separating them from fifth-placed Liverpool and Tottenham in sixth, both of whom have 55 points, although Kenny Dalglish's side have played a game more than their rivals.
Despite Sunday's close scoreline, City goalkeeper Joe Hart felt his side had plenty in reserve.
"It was a bit nervy but I think if we'd needed to step it up another gear, we would have done," Hart told Sky Sports.
"We got the two goals early and I think it's fair to say got sloppy and let them back in it, but I think if needs be we'd have got another goal."
City defender Vincent Kompany, meanwhile, felt the result was indicative of the strides taken under manager Roberto Mancini this season.
"Maybe last season we would have lost points in a game like this, we're really happy because it wasn't easy," he said.
Asked about the increasing likelihood of sealing their place in next season's Champions League and perhaps even closing the five-point gap to third-placed Arsenal, the Belgian added: "It's massive, not just for the group but for the club.
"We really want to achieve this and, why not catch up with Arsenal? We're going to try it."