The Potters sit 16th in the table, hovering just three points above the relegation zone, though Wigan hold a game in hand over them with only five games left to play.
Pulis has been in the position of needing a result on the final day of the season before with Stoke, and has backed his side to pick up the required points - just as they did in the past.
"If it means going to the wire, so be it," Pulis told reporters. "It wouldn't be the first time for me.
|PULIS RUES SLOPPY GOALS
|7/2||Stoke are 7/2 with William Hill to be relegated
"I think they will respond in the right way. We must make sure we are on the front foot. This is a first in my seven years back and we have five rolls of the dice to get the six points we need.
"We need a call to arms to everybody in Stoke-on-Trent because it has been a dreadful run. We haven't deserved to be where we are but we've shot ourselves in the foot and have to stop that."
Stoke face QPR, Norwich, Sunderland, Tottenham and Southampton in their remaining fixtures, and Pulis believes they need another two wins from those matches to secure their Premier League status - pinpointing their lack of goals as their main problem.
He added: "We're looking for 40 points. Forty keeps you up. So we need six points whether it's from the next two, the last two, whatever.
"We have needed to score more goals. Even when we were doing well, we weren't scoring enough goals. We've had great chances and missed them and struggled in both boxes. We've given poor, poor goals away."