A late Pablo Zabaleta goal sealed the result for the visitors and Pulis admitted his side open approach to the game may have handed City the initiative.
He 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 a chance to attack and create chances. I thought they did that well.
"Although we are disappointed to have lost the game, and lost it in the last few minutes, you have got to give City a lot of credit.
"Unfortunately when you come up against the best teams, they need to be a little below par, you need to be right on top of your game and we weren't right on top of our game."