David Moyes does not want West Ham to be reliant on results elsewhere to stay in the Premier League this season, while Michail Antonio is out of the run-in.
The Hammers eased their relegation fears with a 3-0 home win against Southampton last week, but they are still just five points clear of the drop zone and face Chelsea, Arsenal, Manchester City and Manchester United before the end of the season.
Despite that daunting fixture list, Moyes has urged West Ham to pick up the results they need rather than depending on others to slip up.
"It's massively important to be in control of our own destiny and not be reliant on other results," he told a pre-match news conference ahead of the trip to Chelsea.
"We've got Stoke City next weekend, then Manchester City, Manchester United and Everton all at home. I'm hopeful the crowd and everyone associated with the club will play their part in getting us over the line."
If West Ham are to steer clear of danger, though, they will have to do it without winger Antonio, who will miss the rest of the campaign due to an operation on a troublesome hamstring.
"[Antonio] is going to have an operation on his hamstring and the biggest thing now is to get him ready for next season," said Moyes. "We'll miss his great strength and pace.
"He picked up a hamstring injury at the end of last season and has never really recovered from it. He's had some big injuries since I've been here."
Argentina international Manuel Lanzini is doubtful for Sunday's game at Stamford Bridge, too, with Moyes adding: "He's got a medial ligament injury.
"He's able to run in straight lines at the moment. I wouldn't completely rule him out but he's a doubt."