A late Pablo Zabaleta goal was enough to beat the Potters at the Brittania Stadium and Pulis claims that a change of approach from his side suited their opponents.
The Potters manager said: "We played more open than we normally do at home.
"In a cup-tie you want to catch them and have a go at them. You have got to give City a lot of credit. Their attitude and approach was first class.
"By playing as open as we did, against the best teams, it always gives them an opportunity to attack and create chances and I thought they did that well."
Stoke turn their attentions back to the Premier League on Tuesday as they play host to Wigan Athletic.