A 4-0 win over Alan Pardew's side sees the Potters on 37 points, just five ahead of 18th placed Wolves and Pulis thinks that his team must break the 40 point barrier at least, to guarantee themselves safety.
Asked if he thought his team were safe yet, Pulis replied: "No. It might even be more than 40 points now, if you look at the table.
"We've got eight games to go, four games at home. We've got to make sure that we pick points up. We've got two tough games coming up - Chelsea [at home] and Tottenham away - and it's tough. It does look really, really tough all the way through, so we certainly need some more points."
However, the former Plymouth boss was delighted with Saturday afternoon's win and believes his team are moving in the right direction after two important wins on the bounce, after last week's victory over West Ham United to secure them a place in next month's FA Cup final.
"We're pleased," Pulis enthused. "We knew it'd be a tough game. On the back of what we did last week against West Ham there was always that concern that the players might not be focused and may be a little bit drained.
"We're doing things at this football club that have not happened for nearly 39 years and with players that are not used to the pressure of playing in these competitions at the level we're dealing with now. It was always a concern for me this week that the players were focused and together.
"There's times in the season where you do get really pleased, and I was really pleased for them today. On the basis that I knew they'd be a bit drained and maybe not as focused as they normally are, but they were very, very good today."Summer signing Jonathan Walters opened the scoring in the game at the Britannia Stadium and his manager has been pleased with the striker's performances so far after arriving from Ipswich.
Pulis added: "Jonathan Walters has been a very good signing for this football club. He's been excellent in everything. He's grown with the team and the club. He's one of them that takes things on board. The players have got a lot of time for him because of his effort and commitment."
Meanwhile, the home fans were given a worry after club favourite Matthew Etherington was taken off on the hour, but Pulis insists this was merely precautionary.
"There's no problems," the 53-year-old said. "During the week Matty looked tired and there was some thought and some concern about whether we'd leave him or bring him on. It was always going to be that hour and then take him off.
"He's got so much ability, he's so important to us. At times we have to be careful."
Asked if he was happy for a break during the international period, Pulis responded defiantly, stating the need for consistency to keep the results coming.
"We've got momentum now, you'd like to keep it going with what we've done these last couple of weeks. You've got to deal with what we deal with and get on with it."