The Potters have never finished in the top half of the Barclays Premier League since their promotion in 2008, but are eighth and just five points off the top four at the half-way stage of the season.
Stoke qualified for Europe as 2011 FA Cup runners-up but Pulis believes they have every chance of earning a return on the merit of their league position.
"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," he said.
"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 get ahead of themselves after the Boxing Day victory over Liverpool extended their unbeaten league run to 10 matches, one short of equalling the club's top-flight record.
They host struggling Southampton on Saturday and Pulis stressed the importance of remaining focused.
"In many respects the Southampton game will be the toughest of the two because of the raised expectations," he told The Sentinel. "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."
