The striker had been jeered up until that point, but after he curled a sensational strike into the far top corner and refused to celebrate, the Stadio Barbera crowd showed its gratitude.
"I am happy with the applause and was very moved by that gesture. I have never forgotten these fans," he said after the 3-1 victory.
"I am also content with the victory, which was important for our position in the table. We've got to continue picking up points so we can climb the table."
When asked if Napoli are targeting a top three finish, Cavani refused to be pegged down.
"I don't like to set objectives like that. All I know is that we have to win and go as high as possible, whatever that may be. I want to see how far this Napoli side can go."