A maximum points return in February has been undercut by the Hammers failing to register a single point so far in March and the manager is keen to prevent mounting pressure
The Upton Park club looked to be easing clear of relegation trouble following a fantastic February that yielded a maximum return of 12 points from four Premier League matches.
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"There's always pressure that builds when you have a run of defeats," he told reporters. "The anxiety when it's like that is felt all around the ground
"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.
"I think in the beginning, every manager that comes into the Premier League has the anxiety of whether they're good enough.
"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."
The excellent run of form in February moved West Ham into the top half of the table but they are now back down to 14th, with 31 points to their name.
Allardyce believes that a point-per-game average will be enough to secure the club's top-flight status and he is eager to achieve that tally as quickly as possible, with Hull City the visitors to Upton Park on Wednesday.
"We never said or suggested that we were safe when we were on the fantastic run and we've got sucked back towards it again," he added. "We need 38 points and we'll want to go past that as quickly as possible.
"We've had a couple of lapses in concentration that the opposition have taken advantage of in the last three games."