The Georgia star is expected to join PSG in the coming days in a €75m deal.
Giaccherini told Radio Gol: "I think (Antonio) Conte was clear about Kvaraskhelia. If it were up to him, he would be a player to absolutely protect, he tried to keep him together with (Giovanni) Di Lorenzo. However, it is logical that the player has other priorities.
"I think that his contract has been pulled a bit too far, protecting him after the Scudetto to make him increasingly central to the project. Conte's skill is to consider those who play less even more, because he knows that to obtain important results, everyone is needed. Like the Scudetto fight, because let's be clear, Napoli must aim for the championship.
"When injuries and suspensions arrive, there will be a need for those who play less, and therefore everyone will always have to be on the ball. I was trained by him and even when I wasn't playing I was always ready to enter the field, this is Conte's great strength.
"The next matches will tell us if the big matches are the last step that this Napoli must take, winning in the important matches against the other contenders to secure the championship. The next month will be decisive to understand if it can really win the Scudetto."