After dominating proceedings at the Stadio San Paolo, Lorenzo Insigne's late effort was that was needed to crown the hosts' efforts.
The triumph over last season’s Champions League finalists moved Napoli to the top of the group C standings with four points from two games.
And the Senegalese defender has disclosed that Wednesday’s result will give Carlo Ancelotti’s men 'belief' as they bounced back from their disappointing 3-1 loss to Juventus on Saturday.
“We started the season well and wanted to give a strong response tonight, which I believe we did. We gain belief and look forward to the future with more confidence,” Koulibaly told Sky Sport Italia, per Football Italia.
Meanwhile, the 27-year centre-back has backed manager Ancelotti - who was critical of the team’s performance in the defeat to the league leaders last weekend.
“The coach is right, we have to believe in ourselves, as we have a fine squad and many talented individuals too,” he added.
Koulibaly has played every minute of Napoli’s matches this season and was in action for the entire duration against the Reds.