The manager admits the pressure is beginning to build on his team when they run out at Upton Park.
Four of their next five matches, however, are against teams in the bottom seven.
Allardyce said: "We are one of those teams who are struggling with points on the board. All that matters at the end is winning matches. Last season at home was a fantastic ride for us. This season it has been bitterly disappointing.
"The players are bound to feel extra pressure and feel more anxious but they have to remind themselves of the good performances they've given and continue in that vein from a confidence point of view. We have been severely punished for not taking chances.
"We haven't finished teams off when we had the opportunity. We were 2-1 up against Everton but didn't finish it off for a victory. We should have had a 0-0 against Stoke but we didn't."
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