Napoli arrived in Turin on the back of a three-match winning streak in Serie A but fell short of capitalising on several good chances, despite solid defensive efforts.
"I realise the difficulty of getting a draw away to Juventus, a team that was 18 points away from Napoli last season," Conte told DAZN.
"We worked on this system, I am moderately satisfied with the defence, but we could’ve done far better in attack and I think we had the clearest scoring opportunities."
Striker Romelu Lukaku, who had shown been effective in front of goal since joining Napoli recently, struggled against Juve and was substituted near the end.
"I think we did it well with the midfielders. Romelu still needs to get into the kind of shape that I require," Conte said.
"I had asked for consistency and it was a good performance in terms of focus, but we can and must do better when we have the ball, as there were some favourable situations."
Reflecting on his past tenure at Juve from 2011 to 2014, Conte acknowledged the challenge of playing at Allianz Stadium.
"I know it is not easy to play here, which is why I made this stadium a fortress during my time," he concluded.
Napoli host Monza in the next round of games after they face Palermo in the second round of Coppa Italia on Thursday.
