West Ham, with only seven points from their last nine league games, are now down to 14th and looking anxiously over their shoulders.
Allardyce admitted: "I'm always worried until we're mathematically safe. You never stop worrying and are always looking at what could happen. But my belief is that our home record will be good enough to get us safe.
"It's about getting six more points. If we get to 39 points, it doesn't matter what the teams below us are doing."