The attacker, who had some issues with the San Paolo faithful last season, refused to take the microphone during a squad presentation ceremony at Dimaro
The Italy international was offered the chance to speak during the formal presentation of the Partenopei squad for the 2014-15 season at Dimaro.
However, Insigne refused to take the microphone from the ceremony host, prompting boos from some of the supporters present.
The Naples-born attacker had some problems with the San Paolo faithful last season but Inler admits that he was left mystified by his team-mate's actions.
"I don't understand what happened yesterday [Friday]," the Switzerland international told Sky Sport Italia. "It was his choice and only he knows why he didn't want to speak.
"The are very important for us, especially in difficult moments when their help is essential.
"With their support, we will become an even stronger team."
Indeed, Inler believes that Napoli, who finished third in Serie A last season, are capable of challenging for the Scudetto this term.
"We have grown so much in the last four years," the defensive midfielder mused. "We have win two Coppa Italias and now we want to aim higher.
"We're still growing under the guidance of [coach Rafa] Benitez. But I think only game by game and I remain with my feet firmly planted on the ground."