The Staffordshire outfit played their 46th game of a gruelling campaign on Sunday when they were defeated 2-1 at Liverpool in the FA Cup quarter-finals.
Their participation in the Carling Cup was also ended by the Reds, who secured a fourth-round victory at the Britannia Stadium in October, while in the Europa League, Stoke made it through the group stage to the last 32 before being knocked out by Valencia in February.
They now have 10 Barclays Premier League games left to contest and head into Wednesday night's clash with Tottenham at White Hart Lane lying 14th in the table.
The top half - which they are yet to finish in since their return to the top flight in 2008-09 - is only a point away at the moment and with that target in his sights, manager Pulis has stressed how important the role of Potters fans will be in giving his players a final boost.
"We've had a fantastic season, especially when you look at what we've achieved in the cup competitions, but now we just need to get over the line," Pulis told www.stokecityfc.com.
"We still need a few points in the Premier League and we want to finish as high in the table as possible, so at the end of a long season in which we have played 46 games now, we need one final effort to get us to where we want to be.
"The supporters were fantastic once again (at Sunday's match), but we'll need them over the remaining matches to help push us over that line.
"I've said before that the togetherness throughout this club has been key to our success and we need to stick together now.
"The players have worked so hard over the past eight months; their effort and commitment has been excellent, but we now have to finish the job off.
"So I am asking the fans personally to get behind us because the lads certainly need that little bit of help."
Pulis' sentiments have been echoed by Stoke chairman Peter Coates, who says there is still plenty to play for this term.
"It is vital for us to have a good end to the season and pick up as many points as we can," said Coates, quoted in The Sentinel.
"If we finish in the top half, the financial aspect would be attractive and important to us in terms of the running of the club.
"And we should not underestimate the achievement of finishing in the top 10, if we did it, especially after such a long season and with such a large workload of fixtures.
"We also need our fans to be as good as they have always been, because there is still a long way to go."
This match comes just four days after Bolton midfielder Fabrice Muamba suffered a cardiac arrest on the pitch at White Hart Lane.
Spurs boss Harry Redknapp has revealed Pulis offered to postpone Wednesday's game after the traumatic events of Saturday - which led to the FA Cup quarter final between the London side and Wanderers being abandoned - but the fixture is going ahead.
Muamba's condition has improved and Redknapp says his players, buoyed by the news, are ready to play again.
Referring to the situation, Coates said: "It's their home fixture, so it was really a decision for them to make.
"But we are more than comfortable with their decision."