The Potters have endured a torrid second half of the season, prompting sections of the club's support to voice their discontent.
Pulis said he understands their frustration but, after another tepid display, he was adamant expectations must remain tempered.
"The basic line is we should never ever get complacent about being in the Premier League," he said. "We need another six points [to secure safety] and if we do that, it has been another great season for the club.
"There has been bits of moaning and groaning around the place, but the supporters were fantastic today. They really got behind us. They were fabulous.
"You have to accept if supporters are not happy - they pay their money. But staying in the Premier League every year is a massive success."
The draw took Stoke to within two wins of the 40-point mark that is normally seen to represent safety.
Pulis knows his team are lacking confidence and insists a lucky break is all they need to help them return to form.
"We need a break," he explained. "I watched the Everton game [against Manchester City on Saturday] and saw the [Leon] Osman strike - we need something like that. We need a win to give us confidence.
"It [the draw with West Brom] was a very tight game. It gets us off 33 points, which has been a rope around our neck.
"The magic number is always 40 so we have got to get another six points and if we do that I will be delighted.
"It is going to get tighter as the season goes on. We need a couple of wins. We need a break, more than anything else."