Since their promotion four years ago, The Potters have never finished in the top half of the league table, but currently placed eighth, Pulis' men are a mere five points off the top four at the half-way point of the season.
Stoke qualified for Europe as last year's FA Cup runners-up, but the Welshman believes they have every chance of earning a spot on the merit of their league position.
Pulis said: "It's something we should aim for and I'm sure players and fans alike would relish the challenge if we ever got there again.
"That's not to overlook how tough it was with the number and timing of the games and how that affected our league form.
"It takes a lot to get used to games coming thick and fast on a Thursday and then a Sunday, not to mention the fact they kindly gave us away games in the league after virtually every away game in Europe - and they were long trips.
"But having the odds against us is what gets us going as a club, and that includes our fans."
However, Pulis has warned his players they cannot afford to be complacent after their Boxing Day victory over Liverpool extended their unbeaten league run to ten games, one short of equalling the club's record.
Stoke host struggling Southampton at the Britannia Stadium on Sunday and Pulis insists his side must keep their focus.
"In many respects the Southampton game will be the toughest of the two because of the raised expectations," he said.
"Southampton are giving it a good go and they will be a big challenge for us, especially if we are not up for the game.
"The other night was tremendous for everyone, and the players deserved their praise for the wonderful effort they put in.
"But that is gone and now we have to raise ourselves for another challenge."
Defender Geoff Cameron, along with captain Ryan Shawcross, is suspended after reaching five bookings for the season.
The US international is disappointed to be missing out but he is keen to capitalise on the good start the club have made.
"I want to play in every game, just as every other player in the squad does," he told the club's official website.
"Somebody will come into the side and hopefully they will do well and help the lads get the three points on the board.
"We have done well over the first part of the season, been hard to beat and picked up a good number of points, so there is confidence within the locker room.
"It's important to keep working hard though and making sure we keep doing the right things, like we have done over the last few months.
"If we do that, then we can have another good half of the season."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar