Palace may have dug in to earn a replay at Selhurst Park, but it was City who conjured up what few chances there were in a drab tie.
Leicester were robbed by injury of their prolific striker Matty Fryatt, while the Londoners had been weakened in the run-up to the game by a virus.
In the absence of Fryatt, Steven Howard was City's lone striker, supported down the flanks by wingers Max-Alain Gradel and Lloyd Dyer.
And the big forward was the focus of City's early attacks when he flicked a Gradel corner narrowly wide and then headed over a free-kick by the same player.
The lifeless Eagles had only a wayward shot from Paul Ifill before the half-hour mark, when they were almost forced to pay for their lethargy when Bruno Berner touched a free-kick to Joe Mattock, who drove just wide from 20 yards.
Just before the break Jose Fonte was forced to hack away a goalbound shot from Jack Hobbs as Leicester ended the half in the ascendancy.
Soon after the re-start the Foxes survived a penalty scare when the ball struck Gradel's arm before Leandre Griffit's 25-yard drive almost found the target.
Berner made way for Paul Dickov on 58 minutes and the former Scotland international made an almost instant impact with an incisive pass to Howard, who shot wide with just the keeper to beat.
Then Gradel almost broke the deadlock late on when he cut inside a defender, before he unleashed a fierce 20-yard shot which Julian Speroni needed two attempts to smother.
Mattock saved Leicester with five minutes left when he flung himself in front of Neil Danns' goalbound drive, which proved to be the last significant action of a stale game.