A win for Palace would have seen them climb out of the bottom three, but they were unable to open the scoring despite going close through James Vaughan, Paddy McCarthy and Wilfried Zaha.
The Canaries edge into second place in the table. They rarely looked like scoring, but Grant Holt should have snatched them a win with a late effort.
Queens Park Rangers remain five points clear at the top, after a goalless stalemate at Hull City in the day's only other game.
Chances were also few and far between, with Rangers' Ishmael Miller having an effort ruled out for offside.