The visitors looked there for the taking, having shipped seven goals without reply in successive defeats by Sheffield Wednesday and Middlesbrough.
But former Eagles striker Freedman, who was confirmed as George Burley's successor last week, was left frustrated as his side failed to take advantage and missed the chance to climb out of the Championship relegation zone.
Darren Ambrose came closest to finding the net for the hosts when he rattled the post early in the second half, and City's Ivan Sproule repeated the trick at the other end late on.
But with two sides desperately lacking in confidence in front of goal a stalemate was always on the cards.
After a tentative start from both teams, City created the first chance for Brett Pitman.
Jamal Campbell-Ryce sent over an inviting cross but Pitman, looking for his 12th goal of the season, crashed his volley wide.
Palace's jittery rearguard then gave Albert Adomah the time and space to shoot but his effort flew too high.
David James was in the City goal after the club successfully appealed against his red card against Boro, and he was called into action for the first time on the half hour.
Jermaine Easter, making his full Palace debut after joining from MK Dons, drilled a shot in from 20 yards and James made a comfortable save.
Moments later Pitman took aim from 25 yards with a fierce drive which just cleared Julian Speroni's crossbar.
Palace's best opportunity of the first half came shortly before the interval when Pablo Counago's shot was blocked by Damion Stewart and the ball fell to Darren Ambrose, whose curling effort was plucked out of the air by James.
Ambrose, back in the Palace side after another spell on the sidelines, came agonisingly close to breaking the deadlock five minutes after the interval when his 20-yard drive cannoned back off the post with James beaten.
Freedman threw on Steffen Iversen and Sean Scannell in a bid to find an elusive goal.
But instead it was City who almost snatched a dramatic win nine minutes from time when Sproule let fly only to be denied by the woodwork.