The Championship outfit held the Premier League champions to a stalemate at Carrow Road, earning a replay at Stamford Bridge for a second chance to make it into the fourth round of the competition.
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.
"It's a bit frustrating. We knew the difficulty of the game. When you play away in this competition it's not easy. It was a pity, but great commitment from our players. We tried to win the game but we must accept the final result. In the first half we had difficulty to attack but in the second half we created chances to score," he told reporters.
"We have to play another game - the schedule is busy. Norwich deserve to have another game. For us it's not simple to add another game in the schedule. These are the rules though. There is disappointment for the final result, we wanted to win, but I think the game was very tough. Now we have to play another game at Stamford Bridge and Norwich deserved this opportunity, another chance.
"For us it is a small problem as we have to play another game when the schedule is very busy. When you play in this trophy you know it is very difficult, but today the commitment of my players was very good. Maybe in the first half we could be better. We tried to win, but they defended very well and the result was very fair.
"With these players we scored five against Stoke when you play Willian and Pedro they are creative players. We found a bit of difficulty we tried to win the game. Our target was to win the game and to try to avoid to repeat the game. The schedule is very busy, we have to play two games in the Carabao Cup against Arsenal, but these are the rules and we have to respect that."
Chelsea must now turn their attention to their EFL Cup semi-final first leg against Arsenal on Wednesday.