The Welsh manager also delighted with victory over Reds but urges his side to improve technically whilst maintaining their spirit and commitment
The win came courtesy of a contentious penalty after Jamie Carragher was deemed to have illegally brought down Jonathan Walters, incurring the wrath of Kenny Dalglish after the game, with the Scot displeased that his side had seen several appeals fall on deaf ears.
"Kenny [Dalglish] will be as biased as I am. If you're at Stoke City that will always be the case," Pulis said.
"I'll respect his opinion, whether they were [penalties] or not I don't know, but I'll have a look later on.
"I thought we were pretty poor in possession of the ball at times and we are better than that, but we were really top drawer off the ball.
"We worked very, very hard. We stopped them from playing."
The Welsh boss had plenty of praise for Liverpool forward Luis Suarez, who endured a frustrating spell in front of goal but threatened the backline throughout the match.
"I thought [Luis] Suarez up front was absolutely fantastic. He looks a real, real player. A player that will grace the Premier League. His movement and touch at times was different class," Pulis said.
Pulis – who spent over £20 million on deadine day by signing Peter Crouch, Wilson Palacios and Cameron Jerome – admitted that the club must endeavour to improve.
"We need to keep that, we need to get better technically and improve the side, especially from a passing point of view," he said.
"But we still need that spirit and commitment."
The win extended Stoke's unbeaten start to the season to eight games, and the manager admitted he was delighted to have got off to such a strong opening to the campaign, and the Welsh boss admitted he was relieved and proud that his side got through a tough beginning to the Premier League.
"I'm pleased as punch," he said.
"When you look at it, we've got Chelsea, Liverpool and Manchester United as our first three home games, and I was really disappointed with the way that came out.
"This is a fortress and you're playing three of the top clubs in this country. So you're looking at the points and thinking where are the points going to come from?
"Then you've got Norwich away, their first Premier League game, and then we've got West Brom away, a local derby, after European games – so it's been a very tough start, and for us to get eight points and qualify for Europe has been a very good start."
Pulis handed record signing Crouch his debut, and the Welsh boss admitted that his arrival has given the squad much needed depth.
"He was smashing, he never stopped working," Pulis said.
"I think the quality into him has got to be better, and we'll talk about that, but he still plays – he'll improve what we've got.
"The other thing is with the Europa League, with the FA Cup, with the League Cup, we want to do well in all the games we play, so we need depth.
"To be able to bring Kenwyne [Jones] on today and still have Cameron [Jerome] on the side showed that we've got a little bit more depth than we've ever had, and hopefully that'll help us to try and win as many games as we can."