Willy Caballero thanked Kepa Arrizabalaga for his support after the Argentina international was drafted into the Chelsea starting XI at the expense of his rival for the position on Wednesday.
Caballero was in goal for the 2-0 victory over Tottenham, with Kepa dropped following his refusal to be substituted during Sunday's EFL Cup final defeat to Manchester City.
Sarri said before kick-off that he was sending a "message" to his players with his selection that Chelsea are a team and not a collection of individuals.
Caballero acknowledged the furore surrounding events at Wembley had been discussed among the squad in the build-up but insisted Kepa had been gracious in the wake of his omission.
"Always a clean sheet and playing for me is a satisfaction, but we spoke and we listened a lot about what happened the other day," Caballero told BT Sport.
"The very good news is that it doesn't matter what happened, we are ready.
"Also, I thought Kepa was fantastic today, supporting me.
"He has learned, we have learned and we are improving as a team."
Pedro opened the scoring by firing between the legs of Spurs keeper Hugo Lloris, before a calamitous own goal from Kieran Trippier made sure of the three points.
"As a derby it's always important, but also to get three points to be a little bit closer [to the top four], also close to Tottenham," added Caballero, with Chelsea now sixth and three points adrift of fourth-place Arsenal.
"We are coming from behind a lot of teams but we have to play as today, as a final, and for sure we are going to recover well because after the last effort against City and today we prepare very well our legs again."
