Aleksandar Kolarov secured a share of spoils for City in their Group A opener at the Etihad Stadium by cancelling out Edinson Cavani's 69th-minute breakaway goal with a fine free-kick five minutes later.
Mancini said: "I think we can do better in Munich because it is the second game.
"This game was important for us and I think we were nervous - all the club was so nervous.
"I think we played very well in the first half but in the first 15 minutes of the second half we conceded a lot of space to Naples. They were really dangerous and they scored a goal.
"A team like us can't concede goals like this.
"When we lost that goal we didn't have any midfielders in front of the defenders.
"For 10 minutes there we left a lot of space for Napoli players.
"After that I was happy with our performance - as in the first half - when we played very well."