It was the Potters' worst home defeat since their promotion to the Premier League in 2008.
Pulis said: "We're disappointed. Obviously the second goal kills us.
"The goals that we conceded were poor. I'm really disappointed with the penalty as well. I know Robert's got his hand on his shoulder but Mata's legs just collapse and I think it's soft.
"I don't think that was a 4-0 today. It's very hard to take because I don't think the lads deserve to be on the back of a 4-0 defeat for that performance."