Both sides missed good chances in the rain and snow at Carrow Road, with Robert Snodgrass and Adam Lallana passing up opportunities before Grant Holt was denied from the spot
Poor finishing troubled both sides but Holt had a chance to seal the points at the death only to see the Polish goalkeeper fly across goal to palm away his spot kick.
The Canaries had the better of the chances, two of which were passed up by Robert Snodgrass, but Southampton threatened too and Adam Lallana failed to hit the target from 10 yards.
Chris Hughton handed Sporting KC loanee Kei Kamara his first start since joining on loan from Sporting Kansas City after an impressive goalscoring cameo in Norwich's last home match against Everton. Luke Shaw and Jos Hooiveld came into the Southampton defense, while Jay Rodriguez replaced Jason Puncheon on the left flank.
In pouring rain, the Saints had the better of the opening 20 minutes and Mark Bunn made the first save of the match when he pushed Lallana's powerful shot from 20 yards over the crossbar.
Gaston Ramirez had flashed a corner across goal prior to that and threatened again when released by Rickie Lambert, but Bunn anticipated his attempted chip and stood up tall to divert the ball to safety.
Norwich had lacked quality in the attacking third but Snodgrass tested Artur Boruc for the first time with a 25-yard free kick that nearly deceived the Polish goalkeeper.
The Canaries would ramp up the pressure before the half was out despite their frustrating sloppiness in midfield, though, and Grant Holt was twice unlucky to be denied by controversial officiating.
It seemed the striker was onside on the right when he latched on to a chipped pass behind the defense but the flag was raised and the displeasure of the home supporters became even more vocal when Mark Clattenburg was unmoved by a tug on Holt's shirt as he looked to turn home Snodgrass' low cross.
The two sides exchanged remarkably similar chances to break the deadlock just after halftime. Driven crosses from Rodriguez and Wes Hoolahan just evaded Ramirez and Holt and Lallana and Snodgrass could not take advantage of subsequent chances inside the penalty area.
The cutting edge needed continued to be sorely lacking. Jose Fonte denied Holt a tap-in with an important interception from a Snodgrass cross and the striker then failed to pick out Kamara's run into the box.
Lambert then fired over the bar after Bunn had only been able to parry a Ramirez attempt, but Southampton's chances were becoming fewer and further between.
Norwich, though, was pushing for a winner and Snodgrass had arguably the best chance of the match when released by Hoolahan. The Scottish winger attempted to round Boruc but lost his balance at the vital moment and fired wildly off target with the goal at his mercy.
It looked as if it wouldn't matter when Clattenburg pointed to the spot, to the fury of the Southampton players, after a challenge from Shaw on Holt, but the Norwich captain was denied by Boruc's spectacular save.