The Baggies travel to Burnley tomorrow for the first of four crucial fixtures against teams who are also struggling at the wrong end of the Premier League.
Allardyce watched as his players put in the best display of his tenure to draw with Manchester United last weekend.
But they have also secured results at Manchester City and Liverpool this season and not backed them up. And the boss wants his players to prove they don’t just perform when there is no expectancy on them.
“We have to gain a huge amount of points to make up the ground on the teams that are fourth and fifth bottom,” Allardyce said. “We slipped up in big games against Fulham and Sheffield United recently.
“Because of that we are almost at the stage where we are at ‘must win’ which is a sad place to be at this stage.
“It was ‘don’t lose’ at the beginning. Now it’s changing to must-win.
“We wanted four points from Sheffield United and Fulham. We failed miserably in the end.
“Now we go to Burnley and I’m looking forward to the 90 minutes of quality that we can give. We gave 90 minutes of quality against Manchester United.
“So I’m really challenging the players – it’s not going to be a performance that high just because it was Manchester United, is it? That is my challenge to them.
“The performance you put in against Man United has to now happen against Burnley.
“It has to be just as good and sometimes even better – that’s my challenge to the players.”
Allardyce knows Burnley pose a very different – more direct – tactical threat from Manchester United last weekend.
But due to their position in the table, he says Albion have to do everything they possibly can to win at Turf Moor.
“The players have to look at this game in an entirely different way from the Manchester United one – different tactics, “Allardyce continued.
“Burnley are the best team in the league with how they play.
“Every man knows exactly what their job is in possession and exactly what their job is out of possession.
“Sean (Dyche) has been at that club a very long time and it all fits in very nicely, the jigsaw puzzle has almost been finished.
“They haven’t scored as many goals as they normally do, which is a bonus for us. But they still don’t let many in.
“We face an entirely different challenge on Saturday, and we need to meet that challenge otherwise Burnley will overpower us.
“They are in the bottom eight. We have to be ruthless and take the three points.”