The Foxes went ahead after 46 seconds through Sol Bamba, but City hit back through James Milner and Carlos Tevez.
Sven Goran Erikkson's men got a deserved second chance though when Andy King levelled in the second half.
He said: "I think that is a good result for both teams. Leicester played very well. They did not deserve to lose this game.
"For us, it was also important because now we understand that if we want to win the FA Cup, we have to play at 100%.
"When you play against a team in the Championship, it is never easy."