The Potters have been in indifferent form in the early part of the season and currently lie in 14th place ahead of hosting Fulham on Saturday and Newcastle on Wednesday.
Pulis said: "We have played seven away from home and only five at home. We have to make our home games count - that has always been the case at Stoke City since we have been in the Premier League.
"And for the next two home games against Fulham and Newcastle, we are going to need our supporters - we need them to come and really, really get behind the lads.
"They have played an enormous part and hopefully they will do over the next few days."
On the injury problems at the Britannia Stadium, Pulis provided updates on defender Andy Wilkinson, who limped out of Tuesday's 1-1 draw at West Ham and veteran striker Michael Owen (hamstring).
Pulis added: "Andy went for a scan so we'll be finding more out about him. We are a little bit worried that he might have done something to a disc in his back.
"Michael is coming on alright, but I'm not so sure he will be ready for the first game. He might be available for the Wednesday and the following Saturday."