The Partenopei secured a hard fought win against Torino on Sunday after Insigne missed a penalty in the 27th minute.
A late header by Nigerian striker Victor Osimhen was enough for Napoli to maintain their perfect start with eight wins from eight Serie A games.
After the game, Spalletti who's in his first season at Napoli affirmed that Insigne is still the main man to take spot-kicks for the side.
“Lorenzo has a strong bond, especially with his teammates who are helping him. He was sorry for not giving his contribution,” Spalletti told DAZN.
“For me, Insigne will take the next one, then it will be Lorenzo’s turn and then the captain’s,” Spalletti told DAZN.
“When you have strong players in attack, there are more solutions, so you always hope something can happen,” Spalletti said.
“We know [Ivan] Juric well. He is a strong coach, it’s always a battle when you face his teams because they are always prepared defensively.
“I’ve seen an improvement in terms of mentality and compactness. Seeing Politano and Insigne track back is something that unites, gives strength and creates team spirit.
“We have a team of friends. We also want to propose a good football and tonight we were at a very good level. We built, fought and were willing to give what this game required,” Spalletti continued.
“We obtained a big win for our fans who deserve it. We feel the passion for their love for these colours and the team. It was important to feel their joy tonight.”