The closest either side came to a goal was when Russell Martin saw his long-range effort come back off the post midway through the second half.
Newcastle boss Alan Pardew will be happier with the draw after seeing his side lose their last four games in all competitions, while the stalemate also ends a run of four straight Premier League defeats for Norwich.
Fabricio Coloccini started for Newcastle despite widespread speculation over his future and he was rarely tested in the 90 minutes.
Chances were few and far between in a tepid opening half with both sides showing why they are in such poor form.
The only noteworthy effort of the half came in the 18th minute when the ball fell to Gabriel Obertan inside the box and he fired in a snap-shot which was well kept out by Mark Bunn.
Norwich enjoyed some fine approach play in midfield involving Wes Hoolahan and Anthony Pilkington, but all too often their final pass let them down in the last third.
The second half continued in much the same pattern of the first half as both sides struggled to impose themselves in the game.
In a rare moment of excitement Martin picked the ball up fully 30 yards from goal and fired in a volley which came back off the post with Tim Krul beaten in the Newcastle goal.
Krul came to Newcastle's rescue 15 minutes from time when he produced a fine save to keep out Pilkington's close-range effort.
The only bonus for Newcastle was the return to action for Yohan Cabaye after a lengthy spell on the sidelines through injury.
Norwich almost grabbed a winner in the final chance of the game when Grant Holt rose highest to meet fellow substitute Elliott Bennett's cross and his header across the face of goal was just missed by Pilkington at the far post.