Norwich City manager Daniel Farke, on his part, praised his team for putting up an outstanding performance against the premier league defending champions, adding that he was a big believer in the cup.
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.
The first half was an unforgettably forgettable one, with neither keeper being properly tested.
The replay at Stamford Bridge will take place in the week of January 15.
Chelsea did improve after half-time, with Willian injecting some much-needed pace and drive around the box.
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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.
Chelsea defender David Luiz could play for the first time since 22 November after recovering from a knee injury and Charly Musonda could also feature. We dominated. They didn't even have one shot on our goal and we had chances to score.
"Perhaps they had some advantages but we still had our chances". We are a bit disappointed because it is not that often you are so close to beating a giant like Chelsea in the FA Cup.
Conte admitted: "For sure there is a bit of disappointment because we have another match in a schedule that is so busy". When you play in this trophy you know it is very hard, but today the commitment of my players was very good.
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.