Verona stunned the Azzurri via a brace from Daniel Mosquera and a Dailon Livramento goal on Sunday.
Conte later said: “In the first half, there was only one team in it. I don’t think Verona had a shot. Having said that, we immediately let Verona have a shot at the start of the second half, and in the second instance we went behind.
“Then we melted like snow in the sun. What I feel like saying is that we should apologise to the Neapolitan supporters, who follow us with such passion. I am the coach and it is right that I take full responsibility.”
Conte also stated: “I humbly apologise because the second half was unacceptable. A performance that shows we need to work hard in every aspect. I came to Napoli with lots of enthusiasm, with great desire. If I can help Napoli, I will."
He added: "Aside from the transfer market, what is worrying is seeing the second half and how we melted away like snow.
“On the market, one, two, three, four could arrive, as many as the club want to sign. The problems must be faced head-on, and they are not necessarily easy issues to fix.”