Hammers boss Sam Allardyce believes a further six points will secure their Barclays Premier League position for another season.
While goals from Frank Lampard and Eden Hazard were sending West Ham to defeat at Chelsea on Sunday, Wigan Athletic were registering a 2-1 win over Newcastle United.
That cut the Latics' deficit on the Hammers to six points, but Allardyce is more concerned with his side fulfilling their targets, rather than the issues of the clubs around them.
The Hammers now face an international break, but with a home fixture against West Bromwich Albion next on the agenda, Big Sam wants the east Londoners to claim those six points as quickly as possible.
He said: "You're always looking at what could happen and what couldn't, but my belief in our own record and our performances this year say we're good enough to secure the points we need to be safe.
"At the end of the day it's not about Wigan being six points off us, it's about us getting to 39 points. It wouldn't matter what Wigan do then or anybody else. Not all of them will get to 39 points and that's us. Our concern is, forget about what's happening down below - and I know it's difficult, but the bottom line is, no matter how they get on, you get to 39 points or more and you're all right."
Allardyce was left frustrated as his side drew a blank at Stamford Bridge, especially as he felt they had created enough openings to worry the hosts a little more.
However, he did concede that an attacking performance from the Blues, led by the outstanding Eden Hazard, was difficult to counter.
He continued: "We know we've got the talent, and I want the talent to be maximised every game. I don't want them to underperform because I don't think they should. I want them to maximise their performances whoever they're playing and if the best isn't quite good enough at the end of the day, then fair enough.
"To ask a team who are newly promoted into the Premier League to beat a top four team twice is a pretty big ask isn't it? So, we have to be well satisfied that we actually beat Chelsea at our place 3-1 earlier in the season and on Sunday we weren't good enough to take anything from the game."
With two weeks between games, Allardyce is hoping to use the break to nurse some of his walking wounded back to fitness.
He added: "It's always important to get the players who are injured back. Those three [Joe Cole, Kevin Nolan and Mark Noble] would have probably been on the teamsheet from the start on Sunday, so while there's only three injuries, it's to three key players for us at the moment.
"I think that Mark Noble is the biggest worry because he's had a recurrence of the injury we thought we had cleared up after a four-week rest. That's a major problem for us. Nolan is a broken toe and Joe's is a slight hamstring, and I'd expect him to be fully fit and available for West Brom."