Both sides had opportunities to break the deadlock but wayward finishing left honours even.
City showed two changes from the side held by Plymouth, with Kerrea Gilbert in at full-back and Willo Flood replacing the injured Paul Parry out wide on the right.
Michael Chopra hit the crossbar with a speculative shot in the sixth minute, but the offside flag had already been raised.
Then Steven Thompson fired a first-timer that drifted wide of the visitors' goal.
Former Bluebird Jobi McAnuff made space down the right before crossing into the danger area, but Kevin McNaughton headed clear.
A flowing move out of defence gave Thompson a run down the right and his cross was headed goalwards by Flood, but Eagles goalkeeper Scott Flinders grasped safely.
City kept up the pressure and a Flood centre was headed firmly goalwards by Riccardo Scimeca, but Flinders moved quickly to his left to push the ball away.
The dangerous McAnuff raced clear in the 17th minute, but was brought down on the edge of the area by McNaughton, fortunately for the Bluebirds even though the Scot was the last man, referee Mike Jones only showed him a yellow card.
The busy Flood was in most of the action as City kept pressing forward and his deep cross on the half hour was just missed by the on-rushing Thompson.
Flood missed a chance of breaking the deadlock early in the second half, as with only Flinders to beat he scuffed his shot wide.
City nearly paid for wasted chances when McAnuff lifted a header over Neil Alexander, but the ball dropped over the crossbar and out of play.
Midway through the half City had another let-off when Clinton Morrison put the ball in the net only to find the flag raised for offside.
Marco Reich came on in the 75th minute for Ben Watson as Palace sensed a victory could be theirs, while City were forced to withdraw the injured McNaughton in favour of Kevin Cooper.
As the game drew to a close it was Palace who looked more likely to snatch victory as City wasted neat build-up play with wayward crosses and off-target shots.
The draw drops City out of the play-off positions for the first time since August and manager Dave Jones will no doubt be active when the transfer window opens.