Unbeaten in their last three games, the Potters have gone beyond the 40-point mark to guarantee their top-flight status for another year and have also broken into the top 10 as they look to better their impressive effort from last term.
In their maiden Premier League campaign Pulis' team finished 12th on 45 points, but with 43 accrued already this time out and five games still to play, Stoke are well on course to continue their upward trend.
A win against Bolton at the Britannia Stadium on Saturday will confirm that in terms of points, and Pulis is hopeful the league position at the end of the year will reflect their improvement as well.
"Everybody wants to improve and everybody wants to get better, and that is how it should be," Pulis said.
"Our supporters should want that and demand that, (although) I think it is important to look at what we have achieved so far and not forget that.
"We are 10th at the moment - if it finished tomorrow, I'd be doing absolute somersaults.
"To finish 12th and 10th in the Premier League in two years, as well as making the quarter-finals of the League Cup and quarter-finals of the FA Cup, it will have been two great seasons for us."
Having relied heavily on their form at home last season, Stoke have become better all-rounders this year with improved performances on the road, and Pulis believes with a little more luck they could have been looking at an even higher finish.
"We have done better in lots of respects this season, especially away from home," Pulis said.
"Our away form has been very good, and there have been a lot of games away from home where with that little bit more luck, we could have had more victories rather than draws, and could be a lot better off than where we are."
Bolton have endured a far more torrid season, having sunk into the relegation zone under Gary Megson - who was an increasingly unpopular figure among the club's fans - before replacing him with Owen Coyle.
With Wanderers still only five points above the drop zone, their safety is not yet guaranteed. While Coyle's side will continue their scrap for survival on Saturday, Pulis is delighted to be free of relegation anxiety.
He said: "It's lovely that we are not there. We mustn't get blase about what we have done and how quickly we have done it, but the players, supporters and everybody connected with the football club need a real good pat on the back."
Bolton go into Saturday's match having lost four games in a row, but Pulis remembers the tough time his team had in a 1-1 draw at the Reebok Stadium earlier in the campaign and believes Coyle has quality to work with.
"They have got good players. I think when there is a change of manager - they were unfortunate that there was that bad feeling about Gary," Pulis said.
"I think that stunted the start of their season a bit, but when we played them you could see they have got some quality in the team.
"Owen will need this summer to bed everything down and put in place what he needs to push on."
Pulis has a number of injury concerns ahead of the match, with Matthew Etherington - who is in "ongoing" talks about an improved contact - having picked up a knock in training.
Ricardo Fuller is another injury doubt while Ryan Shawcross and Mamady Sidibe are almost certain to miss out, but James Beattie could return.