Chris Hughton's men enjoyed the better of the first half at Carrow Road, and felt they should have been awarded a penalty when James Collins upended Andrew Surman, but referee Chris Foy correctly ruled the challenge was just outside the area.
West Ham also had their chances, with Carlton Cole's early chance blocked and John Ruddy saving from Kevin Nolan.
Both sides, though, seemed to run out of ideas as the match wore on - but on-loan Tottenham youngster Harry Kane could have won it for the Canaries in stoppage time, only to scuff his shot straight at the keeper.
There was an early opportunity for West Ham in the Norfolk sunshine when a corner was only half-cleared and the ball flashed back across the Norwich goal by Matt Taylor.
At the other end, Surman, in for the injured Anthony Pilkington, cut inside the West Ham box after a quick break down the left and curled the ball just wide of the far post.
Surman continued to press the Irons back, with Guy Demel making a superb tackle to halt his charge into the penalty area.
However, on 13 minutes, it was West Ham who made the first clear opening when Ricardo Vaz Te got away down the right and his cross was headed goalwards by Cole, but Russell Martin knocked it off the line, with Taylor lashing the loose rebound wide.
Norwich felt they should have been awarded a penalty when Robert Snodgrass weaved in from the right and was blocked by Nolan as he cut back inside - but, in a sign of things to come, referee Foy was having none of it.
The Irons skipper then almost put his side ahead when he got on the end of Joey O'Brien's cross after the full-back's strong run down the Norwich left, but England keeper John Ruddy made a smart reaction save.
Norwich capitalised on some poor defending as Snodgrass dashed onto a loose ball down the right, but his cutback towards Simeon Jackson in the six-yard box was hacked behind by Collins.
West Ham then produced a series of blocks and saves by Jussi Jaaskelainen from the resulting corner to turn away successive efforts from Snodgrass, Sebastien Bassong, Grant Holt and Surman.
On 33 minutes, the home side went close again as Holt scuffed wide following a knockdown from Snodgrass.
Foy again incurred the wrath of the home crowd four minutes before half-time.
Surman was upended by Collins as he darted into the penalty box, but the Merseyside official correctly ruled the clumsy challenge had taken place just inches outside the line.
Johnson crashed the free-kick into the wall, before full-back Javier Garrido lashed the rebound wide.
Norwich started the second half brightly, with Jackson's 25-yard effort tipped over by Jaaskelainen, who almost joined the Canaries before signing at Bolton.
Snodgrass just off target with a low effort, and Johnson shot straight at the keeper before West Ham made a double change on 57 minutes when Jarvis and Modibo Maiga replaced Taylor and Cole.
Norwich again tested Jaaskelainen when Leon Barnett nodded a deep cross back into the six-yard box and Bassong's looping header was picked out of the air.
As the hour passed, Canaries manager Hughton sent on Steve Morison for Jackson.
The former Millwall frontman tried his luck with a 20-yard effort after a smart knockdown on his chest, but the shot looped over.
England under-21 forward Kane replaced the ineffective Holt for the final 19 minutes.
As the match opened up again, Jarvis, signed from Wolves in a £7million deal, saw his shot blocked after a quick break into the Norwich half following a poor throw-in.
Kane created space for a shot on the edge of the area, but his effort was wide of the mark.
Then in stoppage time, the 19-year-old was played in on the overlap after a quick break, but scuffed a tame effort straight at the keeper.