However, this was a much improved performance and Scunthorpe had keeper Joe Murphy to thank for saving Darren Huckerby's shot with his knees to earn them a point.
City substitute, Chris Martin, was unlucky to see his shot rebound off the inside of the post and that was as close as the Canaries came to that elusive goal.
The visitors kicked off attacking the River End goal and gave as good as they got in the opening exchanges.
Cliff Byrne was booked for halting Huckerby's run with a clumsy challenge and the City left-winger continued to cause problems for the Scunthorpe defenders.
Lee Croft, operating on the right-wing, put in a good cross, but it was cleared for a corner by Andrew Crosby before it reached Dion Dublin's head.
But it was a shot from Scunthorpe left-winger, Kevan Hurst, which brought the first save of the game, David Marshall catching the ball above his head.
Norwich continued to look more likely to open the scoring without producing a clear-cut chance in front of goal, thanks to some timely interceptions by a well-organised defence.
Byrne was rather fortunate to survive until the break after he was guilty of another body check on Huckerby.
He was replaced for the second-half by Izzy Iriekpen, but Huckerby got the better of him in the first minute and when his cross came in Rossi Jarvis brought a save from Murphy with a low drive from 20 yards.
Dublin got his head to a Jarvis corner, but failed to find the target.
Huckerby's shot from Croft's right-wing cross did bring a save from Murphy, and then Jarvis saw his goal-bound shot blocked by a defender's legs.
In a rare Scunthorpe attack, Matthew Sparrow's shot was deflected on to a post.
Within seconds of replacing Jamie Cureton, Martin saw his shot hit the post, while at the other end Jonathan Forte's cross was headed wide by Cleveland Taylor.
Dublin volleyed wide when he beat Murphy to Gary Doherty's lofted throughball.
Ten minutes from time Doherty also volleyed wide and Dublin's glancing header was held by Murphy.
In the dying minutes Taylor's fierce drive hit the side-netting and Murphy kept out Huckerby's goal-bound shot.