Italia 1 0 Napoli 0 (Vicente Iborra 77) Napoli won the first leg 2-1 thanks to Iborras goal and goals from Mauro Icardi and Alessandro De Marchi.
Napoli won both legs 1-0 thanks to goalkeeping by Francesco Totti.
They are now on the road to the next round, away to Udinese on Saturday, with a clash with Lazio on Sunday.
“I think we have a good squad,” said Napoli manager Antonio Conte.
“We have quality players who have a long way to go.
But we have the chance to do well, which is what matters.
We are in good shape.
I think in the last 10 years, Juventus have won five European Cups, three Champions Leagues, and they have won the Serie A title in four of the last five years.
They are a team that is going to be a threat to all other teams.
This is an important game for us.”
The game against Lazio is their first away leg in more than a decade, having not played there since 2011, and Conte said the match against Napoli will be “more of a home game”.
“We want to give a home-ground game a little bit of extra significance,” he said.
“It’s going to have the feeling of a derby between two clubs.
I think this is a very important game.”
It was the second game in a week for Conte after he had to cancel his trip to the UK due to a stomach virus.
Napoli have scored three in three games this season, with two of those goals coming against Udinese.
Napoli beat Udinese 3-1 on aggregate at the weekend, and have been in the top half of Serie A for two years now.
It’s not the only reason Conte was travelling to Naples to take charge of the match, with Lazaro being promoted to Serie A last season, and he is looking to bring them back up to the top.
“I’ve played every match I’ve been at Napoli,” he added.
“I’ve always had a great relationship with the coach and I think we’re all happy here.”
Napolitano said it was a great honour to play for Lazio, but also that he is “happy” to take on his first game at the helm of the club.
“It’s a great honor to take over the role, but it’s also an honour to lead this team,” he told Sky Sport Italia.
I want to play this game for them.” “
The fans are here for the team, for the coach, and I have a very special bond with them.
I want to play this game for them.”
Lazaro are currently seventh in Serie A, six points off second place, with Conte already looking to boost their Champions League aspirations.
The match will be shown on Sky Sport 1 on Sunday at 12:00 BST.
Watch the match on Sky Sports 1