CITY's Premier League plight worsened with a 1-0 defeat to relegation rivals Swansea City at the Liberty Stadium.
There was nothing between the teams in a goalless first half but the hosts upped their game after the break and won thanks to Gylfi Sigurdsson's 61st-minute goal.
The Canaries never got got going in the second half, only fashioning some chances in the final few minutes with Nathan Redmond and Patrick Bamford going close.
They made two changes from Tuesday's 2-1 home loss to Chelsea, with Alex Neil reverting back to the 4-2-3-1 system that has been used for the majority of the campaign.
Steven Naismith replaced Ryan Bennett, with Russell Martin accompanying Timm Klose in central defence and Wes Hoolahan playing off frontman Cameron Jerome. Gary O'Neil replaced Alex Tettey.
Former Norwich pair Kyle Naughton and Leroy Fer were on the bench for Swansea, who made six changes from their midweek victory over Arsenal.
Nathan Redmond was the first player to get a shot on target after six minutes when he cut inside on his left foot before drilling a shot at Lukasz Fabianski.
Swansea were seeing more of the ball, however, and City had to contend with having two players booked early on - Jerome for an aerial challenge with Angel Rangel, and Robbie Brady for a poorly-timed tackle on the same player.
City's bad luck with injuries this week then continued when Brady was forced off on 26 minutes, with Bennett his replacement. Skipper Martin moved across to left-back.
John Ruddy was still to be tested in a half of few opportunities - Wayne Routledge should have got a shot away on 35 minutes but he slipped when found in the box by Neil Taylor.
Jerome forced a save from Fabianski as half-time approached after clever play by Jonny Howson and Naismith, but Swansea will have felt hard done by in stoppage time when they were denied a penalty.
Andre Ayew fell under Klose's challenge in the area, but referee Craig Pawson waved play on.
HALF-TIME: Swansea City 0-0 Norwich City
Modou Barrow came on for Alberto Paloschi at half-time for Swansea, and after a tense opening ten minutes of the half, Alan Curtis made another switch as Fer was introduced to the fray.
Barrow lifted a shot over from close-range for the hosts as City struggled to make any inroads into their opponents, and they picked up yet another booking when O'Neil tripped Fer.
Then, with half an hour left, the Welsh side took the lead with Fer getting the assist, teeing up Sigurdsson on the left, who rolled the ball into the corner beyond Ruddy.
Bamford and Dieumerci Mbokani came on immediately for the Canaries, but Ruddy was called into action when Routledge fired a shot at goal from a very narrow angle.
Bamford was causing some issues for Swansea's defence with his movement but City weren't worrying Fabianski between the sticks.
Mbokani turned a header off target from Hoolahan's cross, but the hosts looked largely in control and City will have been disappointed with their second half display.
Ruddy made a fine one-handed save from Sigurdsson free-kick with six minutes left of normal time, though City did create a late flurry of opportunities.
Redmond guided a shot wide before Bamford was denied by Fabianski at the near post, and Swansea held on for a second victory in four days.
FULL-TIME: Swansea City 1-0 Norwich City
GOALS: Swans: Gylfi Sigurdsson (61)
SWANSEA CITY: Fabianski, Rangel, Fernandez, Williams (c), Taylor, Britton (Fer 55), Cork, Sigurdsson, Routledge, Ayew (Gomis 82), Paloschi (Barrow 45). Subs not used: Nordfeldt (GK), Naughton, Amat, Montero.
NORWICH CITY: Ruddy; Pinto, Martin (c), Klose, Brady (Bennett 26); O'Neil, Howson; Redmond, Hoolahan, Naismith (Bamford 64); Jerome (Mbokani 64). Subs not used: Rudd (GK), Jarvis, Dorrans, Mulumbu.
REFEREE: Craig Pawson