Chelsea took on Manchester City at Wembley in 2019 and the game finished 0-0 after extra-time.
Just before it went to penalties, Kepa went down with an injury and Sarri looked ready to replace him with Willy Caballero.
Kepa caught his number on the fourth official's board and gestured he was fine to continue - shocking his Blues teammates and the coaching staff.
Sarri stormed off down the tunnel and Kepa remained on the pitch - with City managing to win the game on penalties.
The Spaniard has explained the entire misunderstanding in a column for the Players' Tribune, explaining: "It was all a big misunderstanding.
"Manchester City were dominating the game in extra time and there was barely any time left until penalties.
"After making a save, I felt something in my leg and I called for the physio to make sure it was nothing. Above all, though, I wanted to make sure that we as a team could catch our breath.
"Suddenly, I saw that the coach, Maurizio Sarri, had sent Willy Caballero to warm up.
"He thought I couldn't go on. My intention, right or wrong, had only been to waste time to help the team. I didn't have any serious problem that was going to keep me from continuing to play.
"I tried to signal that I was ok, that I wasn't injured. But we were at Wembley in front of more than 80,000 people, so of course Sarri didn't understand me.
"When the fourth official raised the board, clearly I should have come off, and I'm sorry I didn't."
Many accused the 26-year-old of disrespecting his manager and lamented his poor attitude.
But it's clear to see he regretted the entire situation and has apologised to fans and colleagues alike.
He continued: "I was wrong, and I am sorry for everyone who was involved: for Maurizio Sarri, who it seemed like I had undermined in public; for Willy, a teammate and a great professional; and for all my teammates and Chelsea fans who had to put up with everything - all the noise that was generated during the game and then in the days after.
"Inside the club it was no big deal. I had a chat with the boss, we talked about how we had each seen the situation, and we cleared the air. After that I got dropped for one game, but a week later I was back in the team.
"I remember playing a great game against Fulham, and that was it. A couple of months later we knocked Frankfurt out of the Europa League semifinals and I saved two penalties in the shootout. Internally, everything was fine again.
"When I picked up my phone in the dressing room after the League Cup final, I realised that I had become worldwide news. For the next three or four days it didn't stop. It was overwhelming. And clearly, most people who saw the pictures thought that I had disrespected Maurizio.
"I felt misunderstood, because it had never been my intention to snub the coach. I had only tried to tell him I was O.K.. I tried to explain this to the press, but I couldn't."
Chelsea have since signed Edouard Mendy to be their first-choice shotstopper and Kepa is their backup keeper.
Featured Image Credit: Sky Sports
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