The Spaniard refused to be substituted in the closing stages of Sunday's game at Wembley, despite twice going down with cramp.
Sarri wanted to bring on substitute goalkeeper Willy Caballero but was left seething when Kepa refused to leave the field.
After 120 goalless minutes, City went on to win 4-3 on penalties, Kepa saving from Leroy Sane but allowing a weak Sergio Aguero effort to creep beyond him, with Raheem Sterling converting the decisive kick.
Sarri appeared in a much more conciliatory mood when asked about the incident by reporters after the game.
"It was a big misunderstanding,’ said Sarri in quotes published on Chelsea's official website. "I understood he had cramp so I didn’t want the goalkeeper to go to penalties in that physical condition.
"I only realised the situation after three or four minutes when the doctor came to the bench. In the meantime I wanted Caballero on the pitch, and the keeper only wanted me to know he was in condition to go to penalties, so it was a big misunderstanding.
"Kepa was right, even if the way he conducted himself was wrong. Mentally he was right, he was able to go to penalties, but I only realised everything when the doctor was able to come to the bench, not before. I was really angry.
"I want to talk with him because he needs to understand that with a misunderstanding we can get in trouble, especially with you (the media).
"So I think I only have to explain the situation to Kepa but without any other problem."
Chelsea were demolished 6-0 at City in the Premier League two weeks ago but showed a vastly improved display after Sarri used Eden Hazard as a false nine, dropping Gonzalo Higuain to the bench.
"They played exactly how I asked them. Today I am proud of my players," Sarri continued. "You have to ask the club [about his future]. Here I am really very happy.
"In the last three matches we are improving, we have improved a lot. Today we showed to everyone we can become a very solid team.
"We conceded nothing to the opponents and against City it is not easy. So really very happy with my players and proud of my players.
"If you look at the performance it was really very good. In my opinion, against the best team in Europe."