Kone experienced a spiky clash with France teammate Matteo Guendouzi on Sunday, though insists the issues will stay "on the pitch".
He said post-match: "We had prepared the match in this way. We analysed the opposing team, strengths and weaknesses. How they handled set pieces and restarts. We are happy with the victory.
"Honestly, no one spoke to me about how to approach the game from an emotional point of view. I knew it would be a game full of emotions.
"For Roma I knew it was special, I knew what kind of game we were facing. We wanted to win for the fans, the club and the coach.
"Guendouzi? We are teammates in the national team, what happens on the pitch stays on the pitch. I'm sure we'll exchange a message and then start from there."
On coach Claudio Ranieri staying next season, "Yes, why not. He's proving to be a great coach. He's brought out the best in this team."