The Potters are just three points above the relegation zone and dropping like a stone, with Sunday's 2-0 home defeat to Manchester United a sixth loss in a seven-game winless run.
Wigan in the final relegation spot have two games in hand and Stoke's next three games against QPR, Norwich and Sunderland will go a long way to determining their fate.
Robin van Persie converted a penalty in the 66th minute to make it 2-0 to the visitors at the Britannia Stadium after Michael Carrick had opened the scoring from a corner inside four minutes.
Pulis was disappointed with the manner of both goals against United.
"The first goal kills us," he said. "It was a poor goal to concede. The lads have worked well this week and to concede a poor goal - that's the last two home games we've conceded really quickly, the first time the opposition has been in our box.
"The second goal again, the game was tight and that kills it. If Wilko (Andy Wilkinson) stays on his feet, he doesn't concede the penalty."
Pulis still believes two wins from their final five games will see Stoke stay up, with their goal difference better than many of the teams around them.
The Welshman said: "I've just spoken to the players. It's a five-game season. There's eight, maybe nine teams that are in the scrap and we've just got to make sure, no matter what's happened before, the season really starts for us now.
"I still say 40 points will do it."
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- Manchester United