Former Napoli manager Sarri angered players and fans in Naples when he swapped Premier League outfit Chelsea for rival Juventus last month.
Sarri guided Napoli to three consecutive top-three finishes during his time at the club before leaving for Chelsea in 2018.
Insigne was vocal at the time, warning a move to Juve would represent "a betrayal" of Napoli and the club icon stood by his comments.
"I said it and I say it again, for us Neapolitans, that was a betrayal," Insigne said. "Now we have to focus on ourselves and try to beat him. The Scudetto is a dream for all of us and we will try once more."
Insigne's future has been the subject of speculation as he waits to sign a new deal with Napoli.
The 28 year-old – who emerged from the youth team of his boyhood club in 2010 – is contracted to Napoli until 2022.
Insigne has been linked to Paris Saint-Germain and Liverpool previously, and when asked if he could move abroad the Italy international added: "No. I'm still young, I'm happy in Naples and want to stay here for the rest of my career.
"Scoring that goal against Real Madrid gave me such strong sensations and I hope other young Neapolitan lads can feel the same way in future.
"It is the dream of all Neapolitan boys and I am very proud to be in this position."
Insigne made 28 Serie A appearances last season, scoring 10 goals as Napoli finished runners-up to Juventus.