Stoke used their physicality to frustrate City for large spells of the game but were unable to build on that and create regular chances.
Goalkeeper Sorensen said: "We knew we were up against a big side and knew it was going to be tough.
"I thought we gave it everything but sometimes you need that bit of luck. We didn't get the goal that could have given everyone a lift.
"The manager was right in the last 15 minutes to go for the win. We wanted to finish it, not get a replay.
"Unfortunately they overloaded us late on."