Stoke certainly played their part in shaping the relegation battle after losing to QPR last week, and Pulis admitted the nature of Bolton's goals left him thinking they would stay up.
In the 40th minute, Robert Huth's clearance smashed against Mark Davies and flew into the net, then five minutes later Kevin Davies' mis-hit cross caught out Thomas Sorensen at his near post.
Pulis said: "We have a responsibility as a football club, and I think we did at QPR last week, to do the best we possibly can. Irrespective of whether you're playing against friends or whether you've got a soft spot for a team, you have to do your best.
"And I thought in the first 20 or 25 minutes we were really on top. I have to say I came in the dressing room at half-time and I thought it was going to be Bolton's day. They were two bizarre goals.
"But we kept at it second half and the draw wasn't good enough for Bolton. I'm disappointed for Owen and Bolton but it's a reminder to everybody in this league that you have to keep pushing on because it's such a tough league."