Saturday's home loss to Manchester United was their third straight defeat in the Premier League and it left them just six points above the drop zone in 14th place.
Their previous run of four successive wins seems a distant memory as they prepare to host Steve Bruce's promising Hull City side at Upton Park on Wednesday night.
And Allardyce said: "There's always pressure that builds when you have a run of defeats.
"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. We need 38 points and we'll want to go past that as quickly as possible.
"The anxiety when it's like this 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.
"What I have to do is get my team defending as consistently well as they have been and become a goalscoring threat again."
Allardyce has a near-fully fit squad, with just winger Matt Jarvis doubtful for the clash with Hull, but he has previously bemoaned the injuries that have ravaged his strike-force this season.
"In my long time as a manager I've not experienced the ups and downs as we have had, the consistencies and inconsistencies throughout the league," he said.
"Steve has made Hull into a side who have competed all season. He has an array of frontmen who can play as and when necessary. He doesn't have to rely on just Shane Long and Nikica Jelavic."