The victory ensures the Potters enter the draw for the playoff stage of the competition.
"This is the first time this club has played in a European tie and won through, so it's another new bridge which we have crossed," Pulis told the club's official website.
"I'm immensely proud for everyone concerned, but especially so for the Chairman and his family. They have come over with us and I am sure it is one happy family."
City took a 1-0 lead going into the second leg and Ryan Shotton's injury-time winner secured their progression in the tournament.