Aaron Ramsey scored an early opener by finishing off a fine team move and Lucas Torreira's deflected drive, credited as a Kalidou Koulibaly own goal, extended Arsenal's advantage.
But the Gunners have only won twice away from home in all competitions since November, while only Juventus have beaten Napoli at the Stadio San Paolo in over a year.
Arsenal have progressed from eight of their last nine European knock-out ties after winning the first leg, but Ancelotti still feels Napoli can go through.
"Totally confident," the Italian said to BT Sport of Napoli's chances. "We know our support and stadium and we will try to win with two goals.
"We didn't start the game well and the first half was not good. We had difficulties but second half was different to change. We have to try, we have 90 minutes again and we will do everything to try to move on.
"It's difficult to say, it was two different games. First half really bad, second really better. We have to focus on the second half we played and do 90 minutes in Napoli.
"The goals we conceded were two mistakes. First a wrong pass, then the pressure we couldn't control. We were worried at the start and paid with two goals but we have the possibility to change in the home game.
"We could score one goal, but they put a lot of pressure and were dangerous. It's 2-0 and we have to think about the next game."
Ancelotti's opposite number Unai Emery is also fully aware the semi-final is still alive, with Lorenzo Insigne and Piotr Zielinski having missed big chances for an away goal.
"It's a good result but we have a big respect for them away. The first 90 minutes here, we can impose the result and our game plan," Arsenal's head coach said to BT Sport.
"We suffered some times, they can control with possession and created some chances, but we work well in this moment in the season and finished the match.
"We know [there is] another 90 minutes and away there is a different match. We need to be focused, clear and not more confident than we need [to be] to respect them."