The Potters won their first league game of the season at the Britannia Stadium thanks to a brace from Crouch and Pulis was left in no doubt about the importance of the result.
"We are pleased. We've had a real tough start to the season so it is very, very important that we pick points up," he told BBC Sport. "I thought we played really well in the first half and we didn't want half time to come.
"Swansea had a good spell after that but we came back at the end. Peter Crouch was exceptional today and he is unlucky not to have a hat-trick."
Stoke are 12th following the win, with Swansea sitting one place above the Potters.