The Georgia international has failed to match the heights of last season.
Ahead of tonight's Champions League clash with Real Madrid, Kvaratskhelia told AS: "As a footballer, you know that you cannot always live up to what is asked of you.
"You must be aware that moments like this touch you and work to improve your game. Criticism doesn't matter to me, really: I'm only interested in helping the team, it doesn't matter if it's with a goal or an assist.
"Of course, I miss the feeling you get when you score a goal."
The attacker also insists he is happy playing for coach Rudi Garcia.
"First of all, I must thank (Luciano) Spalletti: he believed in me and made my potential explode. I will never have enough words to show my gratitude. From time to time we talk and he continues to support us.
"Rudi is a great coach, we are improving little by little to learn his tactics and vision from him. I am sure that soon we will reach our best version. We are a group available and eager to follow the coach's ideas."