Saints dominated proceedings in snowy East Anglia but could not find a way past Canaries goalkeeper Mark Bunn.
Then, in injury time, referee Mark Clattenburg controversially awarded the home side a penalty but Artur Boruc made a superb save from Grant Holt to preserve the nil-nil scoreline.
And the Southampton manager admitted he was left to breathe a sigh of relief come full time despite his belief that his side's performance deserved three points.
“We leave here semi-happy because the penalty decision could have led to us leaving Norwich having lost the game,” said Pochettino.
“The weather conditions were not ideal for our style of football but the team fought really hard today and the result could have been worse because of the penalty in the last minute.
“It has been hard for us to actually get goals and – on a difficult ground such as Norwich's – I think my team did well and played a good game.
“We were not effective in the chances we created for ourselves but my team played very well and we didn't deserve at all to lose this game.
“In football, there is an old saying that if you can't win then you shouldn't lose and that is what happened today.”
Pochettino also admitted he was unhappy with the decision to penalise Luke Shaw for tripping Holt just inside the box for that missed spot-kick.
“It's not a penalty in my opinion,” he said. “I didn't think it was when it happened on the pitch and I still don’t now I have watched it on the TV.
“The ball was heading out towards the corner and Luke was running after the ball before the opposition [player] banged into him.
“But Artur had a great save and we saved one point, but actually the team deserved to have three points.”
Today’s draw means Saints have taken six points from the last eight games, and Pochettino feels it is only a matter of time until his team hit some real form.
“What is really important for us is that we keep on creating our chances and we have to depend on the effectiveness of our attacking players,” he said.
“That will always come and go, but I am sure that my strikers will score more because we have very talented and skilful strikers.
“We will try to get as many points from our games as possible between now and the end of the season.”