Their best openings came in the second half as Danny Drinkwater shot wide from near the penalty spot and Willian saw an effort turned past the post by Angus Gunn. At the end I think Norwich deserve a replay at Stamford Bridge.
So, the two sides will have to do it all again at Stamford Bridge later this month, an additional game that Conte could do without given Chelsea are still competing in three other competitions. We had an outstanding game and in the first half we dominated, and didn't give a chance away.
Norwich showed promising signs in the early exchanges without every worrying Caballero, only a misunderstanding between the goalkeeper and Luiz threatening to break the deadlock.
However Brazilian defender David Luiz made a return to the Chelsea line-up after being sidelined with injury.
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Chelsea came out with more goal in the second half and had a chance on 50 minutes but Angus Gunn got down well to smother Michy Batshuayi's long-range shot. Normally in 10 games Chelsea will win eight times and it's perhaps one time a draw - but that means there's one special day where you are able to create something special and we're looking forward to doing this.
Conte admitted that he was disappointed with the result and extra game to add to their already busy schedule, but also acknowledged that Norwich were worthy of the draw. "When you play this trophy, especially away, it's very hard".
The last time City went beyond the third round was five seasons ago but there was no sign of an inferiority complex as Murphy exposed the Chelsea backline but fired harmlessly across the face of the goal and another chance went begging.
"Don't forget that Michy is a young player".