The Hammers manager is confident that his side have the quality to survive relegation this season, and is targeting six points to ensure their top flight status
The Hammers' 2-0 defeat away to Chelsea on Sunday was their fourth consecutive loss, but Allardyce is confident that they will pick up enough points to steer clear of a relegation scrap.
"You are always looking at what could happen and what couldn't," Allardyce told West Ham's official website. "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."
Allardyce also stressed his team should focus on winning games, not worrying about the teams below them.
"At the end of the day it's not about Wigan being six points off us, it's about us getting to 39 points." he continued. "It wouldn't matter what Wigan do then or anybody else. Not all of them will get to 39 points and that's us.
"The bottom line is, no matter how they get on, you get to 39 points or more and you're alright."