The home fans were left bewildered and frustrated at their side's disappointing display, the Citizens having beaten title-chasing Chelsea 1-0 in their previous match at the City of Manchester Stadium.
And newly-promoted Norwich, still searching for their first Premiership victory after 11 matches, will have taken great heart following another battling display.
City, who were without the injured Ben Thatcher and Jon Macken, handed a first senior start to Stephen Jordan at left-back while Irish midfielder Willo Flood was handed his first league start.
And City could not have wished for a better start as Flood, a Republic of Ireland Under-21 international, found the net in the 11th minute with a sweetly struck volley, though Canaries keeper Robert Green ought to have kept it out.
And in a bright opening City might have added to their tally had Green not made a couple of decent saves.
Norwich survived City's early onslaught and managed to carve out a couple of decent chances, with Damien Francis twice going close as his side grew in confidence.
City did not heed those danger signs and allowed Norwich to equalise 12 seconds after the re-start.
Danny Mills and Richard Dunne both had chances to clear the danger, but failed to do so, enabling Francis to slot home his second goal of the season.
City produced a spirited finish but Norwich's defence held firm although rather fortuitously at times.
Flood came within inches of scoring a winner for City midway through the half when he was put through by Shaun Wright-Phillips, only to see his angled shot strike the inside of the post and somehow rebound to safety.
And then in the dying minutes Nicolas Anelka burst through on goal only to be denied by Green, while substitute Robbie Fowler's follow-up shot was kept out by Norwich captain Craig Fleming, although there was more than a hint of handball.