The Potters make their debut in the competition this Thursday.
"We've been very successful over five-and-a-half years so we won't be changing," said Pulis.
"We think we play good football. We think we play through the pitch quickly. We have good players who keep the ball and work the ball. We have our own identity. We work on the basis of what the club believe in and what has been tried and trusted.
"Split are probably the hardest draw we could have had and, in some respects, we were looking for an easier ride. But it's a great game for the fans. We'll get a full house at the Brit and I know a lot of supporters are looking forward to going over there."
Shrewdly, Pulis, 53, had fitness coach Paul Maxwell devise a programme that ensured his players would reach their peak earlier than before and be ready for Split.
He added: "Stoke City have started to gain a lot of respect over the last three years. People are starting to look at the club in a different light because we have built it up step-by-step in our own way.
"We have done it the way we wanted to. We won't change now."