Sam Allardyce has set his relegation-threatened Sunderland side a target of four points from their next two Premier League matches.
Michail Antonio's first-half strike was enough to condemn Allardyce's side to a 1-0 defeat on his return to Upton Park, although Sunderland spurned a host of chances to claim a share of the spoils after half-time.
They remain second-bottom of the table, a point from safety, but Allardyce is concerned about a forthcoming weekend away from action on account of Everton's involvement in the quarter-finals of the FA Cup.
As such, he feels there is little margin for error when Crystal Palace head to the Stadium of Light on Tuesday, or when Sunderland make a lengthy trip to Southampton next weekend.
"We've made it a massive pressure game for ourselves on Tuesday night against Palace because we then play Southampton away," Allardyce said.
"We've really got to pick points up out of both those games because after that we don't play for two weeks because we should play Everton.
"That means other Premier League teams around us will play and, if they win, that distance becomes greater and more and more pressure comes on us.
"So in the next two games we'll have to deliver, for me, at least four points. Hopefully we can get more. That's a lot of pressure on ourselves."
On the loss at West Ham, Allardyce felt he did not have to look beyond his own dressing room when it came to apportioning blame.
"You can’t not come away with a result when you've created so many chances," he added.
"We'd have expected Jermain Defoe to have scored, I'd have expected Jack Rodwell to score one of his chances.
"And Patrick van Aanholt, who's been very good at scoring recently, blasted over the bar.
"It's been very difficult to take this result but it's our fault and we've got to live with it."
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