Heading into last Saturday's Barclays Premier League clash at QPR, Pulis was under severe pressure as his side had been sucked into the relegation fight on the back of eight matches without a victory.
But a 2-0 win finally brought relief to all within the club, leaving them now just three points shy of the 40 Pulis firmly believes will guarantee the club a sixth successive season in the top flight.
Pulis, who has this week denied reports he will walk out on Stoke the moment they are assured of safety, knows neither he nor his players can rest until survival is secure.
Ahead of Norwich's visit to the Britannia Stadium, Pulis said: "We've been in a 'must-win-game' situation for the last three or four matches now.
"We've four to go, and we need to get a result in one of those.
"The three points against QPR helped, but we still need to get to 40 points, which has been the target from the beginning of the season.
"I personally think we will be safe with 40, and our goal difference is good, so that's almost an extra point for us.
"The sooner we get to that then the more relaxed we will be, and with a lot more smiles on people's faces. The pressure comes off."