The Potters have slipped into trouble at the bottom end of the Barclays Premier League table after winning just one of their last 13 games.
It is a worrying and unfamiliar situation for the club having made such positive strides since winning promotion to the top flight in 2008.
Supporters have made clear their frustration in recent weeks, and there was regular booing throughout last week's loss to Aston Villa at the Britannia Stadium.
Pulis has also come under fire but the Welshman wants everyone to rally together and recreate the atmosphere the ground is renowned for, particularly as Manchester United visit this weekend.
Pulis said: "The supporters have a right to say what they want to say and do what they want to do, that has always been my philosophy.
"But I don't think there is any reason for people to be moaning and groaning.
"People can talk about the previous seven years at this club and say it has been one of the most successful periods it has had but that counts for nothing.
"It is about today [Friday] and tomorrow [Saturday] - that is what supporters are bothered about.
"They're not worried about what you might have done in the past. It is all about today [Friday].
"But the crowd have been good. There haven't been many occasions at the Britannia over the last six or seven years when they haven't got behind the lads.
"I think they realise we have got three massive games at home and I am expecting the crowd to be absolutely fantastic in those three games."
On the matter of the personal criticism, Pulis is not concerned.
The 55-year-old has experienced enough difficulties in more than two decades of management - a career that has taken him through the lower divisions with Bournemouth, Gillingham, Bristol City, Portsmouth and Plymouth as well as Stoke - to be hardened against it.
"I had it when I was first here and I had it when I came back. It is pretty usual for me," said Pulis, who has guided Stoke to an FA Cup final appearance and into Europe since taking charge for a second spell in 2006.
"It is tough times and you have to accept when you don't win football matches you are going to be under pressure and the spotlight is going to be on you.
"But I try to keep my feet on the ground. You keep working at it and embrace the challenges ahead.
"It is important we stay in the Premier League and important everyone recognises and realises they have to get behind the club and get behind the team now. This is when we need them the most."
Stoke are just three points above the bottom three heading into the latest round of fixtures.
Given their form, a game against runaway leaders United, who are smarting from a derby loss to Manchester City, is a daunting prospect.
Pulis hopes his players can shake off their lethargy and rise to the occasion.
He said: "It is a game that we look forward to. It is one of the reasons why everybody gets excited at being in the Premier League.
"To pit your wits against Sir Alex Ferguson and Manchester United is just fantastic for this football club.
"We have given them good games at our place over the past years and it was a tough game last year, when we got a good draw.
"They have just lost against Manchester City and I am sure he'd have been after them this week, so we know it is going to be tough."
Pulis has set only one target for his players - 40 points - and to achieve it they need two more wins.
He said: "I don't think you can pick a game and say that is going to be a stick-on three points, or a stick-on lose.
"We have got six games to go, 18 points to play for."
Midfielder Glenn Whelan will return after a back problem while winger Matthew Etherington and defender Marc Wilson will be assessed after knocks.