An early strike from Michael Carrick and a second-half Robin van Persie penalty ensured the league leaders left the Britannia Stadium with all three points, but the result means Stoke has still claimed just one league win in 2013.
Despite that terrible run of form dragging the Staffordshire side into a relegation scrap, Pulis remains upbeat about his team's chances of getting six more points in its five remaining Premier League games.
"I'd still say 40 points [will mean survival]," Pulis told reporters. "We've got a pretty good goal difference, so for us if we got to 40 points with the goal difference [we would be safe].
"I've just spoken to the players, it's a five-game season, we've got Manchester United out of the way and there's now eight, maybe nine, teams in the scrap. The season starts for us now and it's very important that you remain positive.
"I think we've got good players, we just need a break. Today we've given two sloppy goals away, we got ourselves back into the game against Aston Villa and [Matthew] Lowton smashes one in from 35 yards.
"We just haven't had the breaks and that's what happens on runs like this. The most important thing is that we all stay positive, and it's difficult to do that. What's gone is gone, the important thing is looking to the next game and the next game.
"The first goal kills us. It was a poor goal to concede, the lads have worked well this week and to concede a poor goal [was disappointing]."