The Stamford Bridge ‘keeper was relatively quiet in a game that, with numerous chances, the Blues should really have won.
Andre-Villas Boas’ team have now kept three clean sheets in a row, but Cech believes that is immaterial if they cannot get wins out of solid defensive displays.
“We would rather have a 3-2 score and get three points," Cech told Chelsea TV.
“That is the reality of the game and I think we played much better than 0-0 suggests because we created enough, had a lot shots and put a lot of balls inside the six-yard box.
“But unfortunately the only thing that we missed is that we didn't put the ball in the back of the net.”
The Czech Republic international has now kept an astonishing 170 clean sheets in 341 appearances for the Blues.
Despite his insistence that Chelsea had the chances to win and should have done so, he reserved praise for Paul Lambert’s Canaries and the way they made it difficult for Villas-Boas’ side.
“We dealt quite well with Norwich's style of playing. One thing they can do really well is to break the game into two parts from side to side,” he conceded.
“Sometimes it is quite hard to shuffle across and stop crosses but we dealt really well with crosses.
“Defensively we did well and attacking we did well as well and it was one of the better games we played this season.”
Cech will be hoping for improvements in the attacking side of Chelsea’s play when they travel the short distance through London to face QPR in their FA Cup fourth round tie at midday Saturday.News Now - Sport News