Caballero benefitted as Kepa was left on the bench for the 2-0 win over Tottenham on Wednesday night, with the latter having refused to leave the pitch when head coach Maurizio Sarri tried to replace him with the former Manchester City stopper in the closing stages of last Sunday's cup final.
Sarri said before the victory over Spurs that his decision to leave Kepa out was "a message to the group" , and came after the keeper had been fined a week's wages.
Caballero told BT Sport after the win: "A clean sheet and to play for me is a satisfaction. We spoke about what happened the other day. The good news is that it doesn't matter what happened. We are ready. Kepa was fantastic today supporting me. He's learned, we learned, and we are improving as a team."
The Italian said after the game: "Caballero is a good goalkeeper with great experience. He's a great man. For us, he's very important on the pitch and in the dressing room."
Asked if the result would lift the morale of his squad, Sarri added: "I don't know. Because as you know we need consistency. We played very well in the last match, in the final. The result was disappointing but we were confident because the performance was a very clever performance. Of course, today is better."
The former Napoli boss also insisted he has always been confident his players will carry out his instructions on the pitch.
"I was sure of it before the match.
"I was sure. My relationship with the players is very, very good. In the last month, even better."
Chelsea kept a clean sheet and Caballero was not called into action once by Spurs' forwards as Tottenham failed to register a shot on target.