Stoke, the runners-up in the FA Cup last season, responded to Danny Kedwell's 16th minute strike with goals from Jon Walters, Cameron Jerome and Robert Huth to ultimately reach the fourth round with ease.
"When it came out of the hat it was a draw you thought was set up for it (an upset)," Pulis said. "I thought we started really slow and couldn't get into the game. When they scored you think 'blimey, let's hope we're not on the end of one'.
"But from that point we gradually took over, we missed some great chances before we actually scored the opening goal. After Cammy scored it was a case of making sure we kept nice and steady. We knew we'd have to defend a lot of balls in the box and we did that with Robert Huth and Ryan Shawcross, who were fantastic."
Pulis managed Gillingham between 1995 and 1999, guiding the club to the brink of the Championship before leaving in acrimonious circumstances, which ended in a court case. Gills chairman Paul Scally wrote in the match programme that he could never forgive Pulis - but the home support gave him a standing ovation.
"If he (Scally) wants to say stuff, it's a free world. He can say what he wants. You've seen who really counts and that's the supporters," Pulis said. "You've seen what they think of the job I did here. That's all that matters to me. It was very special."
Stoke last week