Before victory over Verona, Conte announced the Georgian star had made a transfer request.
After Sunday's win, the coach said: "I want to underline one thing, because it seems to me that I am speaking in Italian. If I were in England I would have some doubts that perhaps with English someone would not understand me. I spoke of disappointment, not towards the player or the club.
"My disappointment because I have not been able to make an impact in these six months so that something changes. It is not that Kvara has disappointed me or the club has disappointed me. I do not put the responsibility on others, I always take it on myself. I thought I could have had an impact in these six months in a different way, instead I realized that we were back to square one.
"I saw headlines today 'Conte disappointed with Kvara', I'm not disappointed with Kvara. I'm disappointed with the situation because I wasn't able to make an impact. A coach of a certain level also helps the club make decisions, advises certain players to take. And when I realize I'm not being incisive, like in this case where we're back to square one, that's my disappointment. Without taking anything away from Khvicha, who is a very good guy.
"Then everyone has to decide their own destiny and the club has to make its decisions. Maybe I was also a bit presumptuous because I thought I would have a bigger impact, but I didn't manage it.
"It's a shame because we're talking about a strong, important player. But we also need to understand the reality of the facts. Having said that, today Khvicha is a Napoli player, let's not forget that because there are steps to take in the event that someone wants to buy Khvicha, nothing is a given. We'll see what happens."