Chelsea's chances of silverware lie mainly in domestic cup competitions, with the Premier League seemingly out of reach and Barcelona lying in wait in the Champions League. A visit to Carrow Road was never going to be a simple task, the hosts enjoying a slight upturn in form in recent weeks
David Luiz returned for Chelsea, making his first appearance since November and the Blues back line were largely untroubled by the Championship side, barring a bright spell before the break.
Chelsea looked disjointed and sluggish in midfield, struggling to create much in the final third. Norwich defended well and created some openings and, despite failing to take advantage of Chelsea's lethargic state, they certainly ended the first half the better side.
However, after the break it seemed Conte's stern words were still ringing in the ears of the Chelsea players, who enjoyed their best spell of the game. Claiming possession and knocking the ball around higher up on the pitch, they began to open up the hosts.
Willian was heavily involved as he burst forward with menace, forcing Gunn into action with a couple of low drives and teeing up for Drinkwater to slice his finish wide of the mark.
The hosts never let up and they matched Chelsea's desire to go forward, albeit only troubling Willy Caballero with a couple of half-chances in the second period. With the clock ticking, Conte brought on Alvaro Morata for Michy Batshuayi, who wasted a golden opportunity with a far from standout performance.
A late surge from Chelsea
A trademark David Luiz free-kick from 30 yards had the crowd on the edge of their seats as it dipped onto the roof of the net and another long-range effort from Zappacosta almost became a stunning stoppage-time winner but it whistled inches past the far post.
Norwich earned a merited replay which will take place on January 16 or 17, and Antonio Conte will hope his men can seal the deal then.