The Blues signed Kovacic on a season-long loan from the Liga giants as part of the deal that saw goalkeeper Thibaut Courtois go the other way.
And, having helped Sarri's side maintain their winning start to the season, the midfielder revealed he is thrilled to be working under former Napoli boss Sarri.
"I am happy because of victory, the most important is that team played good," Kovacic told Sport Klub TV.
"I feel fine, I miss rhythm but I just joined the team. I am working fine and improving.
"It was important for me after three years without continuity of play in Madrid, to find a team and coach that want me, and that happened in Chelsea.
"The club who wanted me and the coach that believes in me. That is what I need.
"Sarri knows me for a long time and I watched a lot of his matches. He loves to play, the team is great, with a lot of big players. I don't expect it to be hard for me to adapt."
Kovacic will be hoping to continue his revival under Sarri when the Blues face Newcastle United at St James' Park next Sunday.