The 25-year-old opened the scoring with an opportunistic strike after just eight minutes of Wednesday's game at the Santiago Bernabeu, before Napoli were swept aside by a dominant Madrid performance and goals from Karim Benzema, Toni Kroos and Casemiro.
Insigne claimed Madrid's experience of games at this stage in the competition was a factor in their victory, but he predicted that Napoli would fight their way back into the tie in the second leg at Stadio San Paolo.
"The result clouds the real performance, but we are alive and kicking, you will see," Insigne told Corriere dello Sport.
"Napoli will amaze you. We'll find ourselves again, the side the people are accustomed to seeing. I also want to add that the 3-1 result lulls you into a false sense of security, because the gap was not so wide on the night.
"Real Madrid players are at the top level, but they are not monsters. We lacked something, perhaps a certain calm needed to express ourselves in our usual style, but there were times where we were able to pass it around and create chances.
"We are the same Napoli side who went unbeaten in 18 matches. The side who went into the break 1-1 with Real Madrid.
"I don't think it was the stadium, but rather the fact Real are more accustomed to playing this type of match. They have it in their DNA and have won every trophy.
"We are on the right track, but still need to grow and to do that we have to go through games and disappointments like this."
Insigne described a pre-match speech by Napoli and Argentina legend Diego Maradona in the changing room before the game as "a unique experience".
He said: "You look at him and realise you are standing next to one of the greatest players of all time.
"He didn't say much, just to do what he failed to achieve 30 years ago. He said it was our turn now and we must believe."