The visitors took the lead through a Steven Gerrard penalty awarded after just 32 seconds after Ryan Shawcross had pulled back Luis Suarez.
Two Jon Walters goals, either side of a Kenwyne Jones header, secured all three points for the Potters and lifted them above Liverpool in the Premier League table.
"It was a great result and performance," Pulis said. "I thought the response after going a goal behind after just 30 seconds was absolutely fantastic and epitomises what the group are about at the moment.
"We've played games where we've created more chances and finished 0-0 so we have been creating the chances but not been taking them.
"We have tremendous respect for Liverpool and we are very proud to host a game against such a great club and when you beat them it gives you great delight, it is always special."
Walters' second, controlling a flick-on from Jones on his chest and volleying past Pepe Reina, was the pick of the goals and took him level with Ricardo Fuller as the club's all-time leading Premier League scorer with 18.
"It was a great finish and I am very pleased for Walts," Pulis added. "His commitment to the group is fabulous and he is a good player as well."