Rudi Garcia's men will take a lead into the second leg of the semi-final tie at the Stadio San Paolo after emerging victorious from an enthralling encounter at the Stadio OIimpico.
Gervinho scored the winner two minutes from time after a Morgan De Sanctis own goal and a strike Dries Mertens had levelled matters for Napoli following earlier goals from the former Arsenal winger and midfielder Kevin Strootman.
The tie remains finely poised because of Napoli's two away goals, but midfielder De Rossi believes Garcia has instilled a mental toughness within the capital club.
"It was a great advert for sport and wonderful to play against such an open team. We must compliment Napoli, as they have a lot of quality and kept fighting," De Rossi told Rai Sport.
"It wasn't easy to concede a goal like that straight after the restart, but after 2-2 we replied very well and won a very difficult game.
"To win 3-2 is very important, certainly compared to the possibility of taking a 2-2 to Naples.
"We've always had the technique and the quality over the last two years, but we missed the right mentality. That is something the coach has given us and we players have fed, helping it to grow so that we can play games like this.
"We can make mistakes, but now we get up and fight back."
The second leg of the last-four clash takes place next Wednesday.
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