Crouch cancelled out the Turkish side's opener before winning the penalty that Jonathan Walters scored to earn the three points.
"I was particularly impressed with the work Peter got through off the ball and the way he defended some of the crosses which were put into our box when we were under pressure," said Pulis.
"It was that work rate which really wore Besiktas down in the end and it's remarkable that we have done that off the back of a tough game against Manchester United."
Pulis also described the England international's influence off the pitch.
"The players have really taken to Peter and he is a great lad in the dressing room," he added. "Considering what he has achieved in his career, to come here and be a part of what we've got while also being as humble as he has been is absolutely fantastic."
The win has taken the Potters to the top of Group E.