The Potters were plunging towards the Premier League relegation zone until last weekend, when a 2-0 win over QPR brought them within three points of the 40 that Pulis feels are needed to stay up.
Pulis rejected talk earlier in the week that he was going to leave once safety has been secured and he was keen to stress that no-one will be resting on their laurels until that happens.
The first of those remaining games comes on Saturday at home to Norwich and 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.
"The players got what they deserved last weekend. I keep saying it, but we've played better away from home but not got the results, which eats away at confidence.
"Winning at QPR has given them the confidence and belief again that we took into games, but never took out of them because of results, and results are everything.
"We needed those three points, but we still need three more, and until we get them no-one will be relaxing here."