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.
But this month has seen a return to the kind of form that saw Allardyce's men slump to 19th in the table on New Year's Day.
Losses at Everton and Stoke City preceded Saturday's home defeat to Manchester United and Allardyce, who said he had never known a campaign quite like it as a manager, admitted that pressure could be playing a part.
"There's always pressure that builds when you have a run of defeats," he said. "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."
The hosts face a late decision on Matt Jarvis for the clash against Hull, with the midfielder having suffered a thigh problem in the 2-0 defeat to United.
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