Reds manager Kenny Dalglish was unhappy with a number of decisions made by match official Mark Clattenburg during his team's 1-0 league defeat at the Britannia Stadium in September.
Pulis' feelings were then similar after the Potters were beaten 2-1 at the same venue by the Merseysiders in the Carling Cup the following month.
The Welshman's criticism of referee Lee Probert on that occasion led to him being warned as to his future conduct by the Football Association and handed a £10,000 fine, which he subsequently appealed against and is still waiting to hear further news about.
There has been more controversy involving Liverpool this week after a two-footed tackle by Reds defender Glen Johnson on Manchester City's Joleon Lescott went unpunished, and Pulis does not want such issues to be at the fore once more in the game on Saturday.
"I think with every game you go into, you hope it is won and lost by the players," Pulis said.
"You hope that referees don't affect it in terms of decisions that change a game of football.
"That is all you hope for, but they are human beings and they will make mistakes like every player and manager does."
Despite the Johnson furore, Liverpool will go into the Stoke match on a high having won at City on Wednesday night to take a 1-0 lead into the second leg of their Carling Cup semi-final.
They have also been buoyed by the news that captain Steven Gerrard - back in the Reds team after a lengthy period dogged by injury - has signed a new contract extension, and Pulis is in no doubt as to the England midfielder's quality.
"Steven has been one of the outstanding players in the Premier League over the years," Pulis said.
"Kenny and the Liverpool supporters will be absolutely delighted to have him back. He has had a long time out and they have missed him.
"In some ways, the rest might have done him the world of good - he might come back a better player."
For Pulis himself, the game marks 400 matches in charge of Stoke.
The 53-year-old has enjoyed huge success during that time, guiding the club to promotion to the top flight, an FA Cup final and the Europa League, and Pulis has been keen to pay tribute to the support he has received from chairman Peter Coates.
"I've been very fortunate to manage this football club for that period of time and it is smashing to do it (reach 400 games) at Liverpool," Pulis said.
"I've been very lucky to work for a chairman that understands football and understands the importance of stability.
"When you have got that backing, it gives a little bit more of a sense of security, and thank goodness that is what has happened.
"There are good and bad times with everything you do - the important thing is just to stay as level as you can and keep driving forward."
Pulis said earlier this week that he would consider managing his native Wales for the memorial match for Gary Speed against Costa Rica next month if asked, but stressed on Friday that he was not pushing for the job.
"I've no burning ambition at this present moment to be the manager of the Welsh national team," Pulis said.
"If Gary's family asked me, I wouldn't say no to that, but I'm sure Wales have people much more qualified than me and would do that job better than I would on that night.
"I don't expect a phonecall - but if it came, then I'd speak to Peter about it and we'd go from there."
Pulis has concerns ahead of Saturday's contest over defenders Jonathan Woodgate, Marc Wilson and Ryan Shotton, who are all nursing what he describes as "niggles" and will be assessed.
Andy Wilkinson could return at the back having overcome his recent knee injury, while the likes of goalkeeper Thomas Sorensen, winger Matthew Etherington and striker Peter Crouch are set to be restored to the team after they were rested for last weekend's FA Cup victory at Gillingham.
Meanwhile, Pulis has revealed that he "won't be taking" VVV-Venlo striker Michael Uchedo after the 21-year-old Nigerian spent some time this week training with the Potters.