Kenny Dalglish's side hit the woodwork three times among several other chances but had only Craig Bellamy's late first-half goal against his former club to show for their efforts.
And a side which has kept only two clean sheets all season should have known what was coming as a result
They were punished on the hour when Grant Holt headed home just three minutes after coming off the bench to spoil what would have been perfect story for Bellamy on his first Liverpool start since May 2007.
The Wales international left Carrow Road 11 years ago and on his travels around various clubs in the Premier League spent one season at Anfield.
He admits he returned this summer with unfinished business and appeared to have resumed his mission in ideal fashion with his first league goal of his second spell.
However, what he could not count on was a defence which has so far only kept clean sheets against Arsenal and Everton, both of whom had been reduced to 10 men, and neither of which has been at Anfield.
Norwich were undoubtedly encouraged by this statistic and looked much more of a threat once they had drawn level.
The omens were good for Liverpool before kick-off as they had won their previous four meetings against the Canaries, although the last of those was in January 2005.
Had it not been for the woodwork the Reds would have enjoyed a much more comfortable evening as twice within the opening 12 minutes they came within inches of scoring.
With less than two minutes gone Martin Skrtel's glancing header from Charlie Adam's right-wing corner crashed against the crossbar.
Luis Suarez's first sight of goal saw him uncharacteristically miss the target from the left side of the penalty area with an ambitious shot with the outside of his right foot.
But the Uruguay international's next effort required the combined efforts of John Ruddy and the frame of his goal to prevent him breaking the deadlock.
The Canaries goalkeeper had to be at full stretch to get his fingertips to the shot and deflect the ball onto his left-hand post.
Norwich briefly threatened when Wes Hoolahan's shot and Steve Morison's header were both fumbled by Jose Reina, although in between that Suarez had fired across goal in front of the Kop.
Apart from that brief spell Norwich, who had won three of their last four matches, had to play second fiddle to a Liverpool side who dominated but came up just short in the final third.
But just when it seemed the hosts had failed to take advantage Bellamy struck in first-half added time.
Suarez's nuisance factor in the Norwich defence saw him tussle with Russell Martin, allowing the ball drop to Bellamy on the edge of the area and his low shot took a deflection off Tierney on its way past Ruddy.
The woodwork denied Liverpool for a third time in the 51st minute when Suarez's run left Leon Barnett baffled but the Uruguay international's shot deflected off Martin and onto the post.
However, within three minutes of Holt coming off the bench he had punished the Reds for failing to take their chances.
The striker powered home a 60th-minute header after Reina came for - and missed - Anthony Pilkington's cross with Jamie Carragher and Glen Johnson in close attendance.
Holt almost doubled his tally six minutes later but this time Reina dealt with his far-post header and, as the game opened up, Ruddy was relieved to see Suarez's toe-poke roll behind after squirming through his fingers.
Suarez's 78th-minute shot was turned past the far post by Ruddy with Gerrard lurking outside the six-yard box as the hosts tried to make up for missed opportunities.
Substitute Andy Carroll's header in the fourth minute of added time summed up Liverpool's match as he powered wide from six yards.
As if to rub salt into the wounds Ruddy produced a brilliant save to tip over Suarez's volley even later.
But like against Sunderland on the opening day of the season and - to a lesser extent - Manchester United last weekend a failure to take their chances cost them the win.
Such dropped points could dearly cost Liverpool's bid to regain Champions League status.