Three consecutive defeats have left the Hammers six points clear of the relegation zone with eight games left to play.
Allardyce now wants his team to forget the possibility of dropping out of the top flight and concentrate on getting enough points to stay up.
"There's always pressure that builds when you have a run of defeats. The anxiety when it's like that is felt all around the ground," he told the club's official website.
"You have to cope with that anxiety, don't let it prey on your mind and go out and play as you know you can.
"In my long time as a manager I've not experienced the ups and downs as we have this season, the consistencies and inconsistencies throughout the league."
West Ham continue their Premier League campaign on Wednesday when they welcome Hull City to Upton Park.