Defeats in their opening two Premier League matches, against Manchester City and Sunderland, have already put pressure on the squad.
Allardyce cannot contemplate a third successive reverse, and that means tightening up at the back.
"We must get a clean sheet against West Ham to give us the basis to build our first league victory on," he said.
"The pressure starts mounting from the moment you start losing matches, whether it is the beginning, middle or end of the season.
"When you lose two on the trot the pressure builds and you can't let it get to three.
"We have to do our very best to win the game and if we can't we have to make sure we don't lose it."
Allardyce will not under-estimate Gianfranco Zola's side but he knows this is a game which is winnable, having dominated their 1-1 draw at Ewood Park last season.
"I think West Ham are always going to be a team that will test you," he added.
"What we have to do is repeat the performance we gave here last year when we were absolutely outstanding but came out with a draw which should have been a resounding victory.
"We need to repeat that performance and become more clinical in our finishing and get those three points we are all looking for."
A much-changed Blackburn side were comfortable 3-1 winners against Gillingham in their midweek Carling Cup second round tie.
Allardyce is likely to shuffle his pack again, with new signing Pascal Chimbonda coming into the squad having completed his move from Tottenham last night.
The Rovers boss said the effects of a first win of the season had lifted spirits.
"It was a great relief. Winning any match is always a pleasure - it is what you are paid to do as a player and a manager," he said.
"From our point of view we were very comfortable indeed and only had to worry about what we considered a poor refereeing decision which let Gillingham back in the game for a short period of time.
"But we overcame that. We missed a load of sitters again, which is what we have been doing, so we still have to brush up on our finishing qualities."