The Potters face Bolton at Wembley on April 17 and Webb, who took charge of the World Cup final in South Africa, has been named as the referee.
Puilis believes Webb is "a great ref" and has backed the referee to ensure there are no controversial talking points in the aftermath of the tie in the capital.
He told the Sentinel: "Howard is a great ref in my book and certainly as good as there is.
"We are pleased to have him. Now we just hope it's an eventful game for the right reasons and that major decisions are decided by the players, not the officials.
"What makes him special is that little bit of an aura he has about him. He deals with players very well and I think most people in the game respect him."
Stoke have only been beaten three times in the 17 Potters games Webb has been in charge of since 2001, Mike Dean will take charge of the other semi-final between Manchester United and Manchester City on April 16.