The Potters were made to take just one point with them after leading after defender Robert Huth struck his first goal for the club but Pulis was content that his side were able to turn the tables on last season's result against the Toffees.
"Last season we were beaten and over-powered at Everton, but this time we have shown great character and deserved the point," Pulis said.
"You have to stand up and be counted at places like this, and that is what we did. I am very pleased with the performance.
"We are happy with a point and it was a much better performance to the one that saw us lose to Manchester United last weekend.
"The players were more committed, we defended very well when we had to.
"Last season we were absolutely murdered here, but this time we have taken a few punches and kept getting up. We were smashing."