Pablo Zabaleta netted the only goal five minutes from time in a re-match of the 2011 final and Pulis accepts that City were deserving winners.
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 an opportunity to attack and create chances and 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, and you need to be right on top of your game and we weren't right on top of our game today."