Sarri benched Kepa -- who was fined one week's wages by Chelsea on Tuesday for refusing to be substituted in the closing stages of the Carabao Cup final -- for the visit of Spurs, with Willy Caballero keeping a clean sheet in his place.
Chelsea responded with an impressive performance to beat their bitter London rivals, with Pedro breaking the deadlock in the 57th minute before Kieran Trippier settled the match with a comical late own goal.
- Ratings: Pedro 9/10 as Blues, Sarri stun Spurs
The incident with Kepa was widely viewed as undermining Sarri's authority and several reports this week claimed members of the Chelsea squad had sided with their goalkeeper over their head coach.
But speaking to ESPN after the Spurs win, Pedro insisted: "There has been a lot of talk this week and that always destabilises [things] a little, but the truth is that in the dressing room we are together, as a great team.
"We have not given much importance to everything that has been talked about and in the end that is the most important thing. We are focused on doing well in every game to get the three points, because from here to the end of the season they will be all finals and we will try to fight to be in the top four.
"This was a great match for us to gain confidence and stay there [in the fight for the top four].
"We have all talked to each other in the dressing room. We've also talked to Willy and we've talked to the coach. The truth is that we have solved all the problems and I think it has been a [small] incident rather than a serious problem.
"It always serves to learn. We are with Kepa, with Willy and with the manager. This is the path that we have to follow. Now we need to get ready very well for the match against Fulham because it is another final."
Sarri justified his decision to bench Kepa by describing it as a message to his players, and Pedro is adamant that doing so will not diminish the Italian's standing with his squad.
"We have always been with him," the Spaniard said of Sarri. "We have always talked about all the problems we have had.
"[Sarri] had to make a decision. He has done that and we simply respect him because we always respect all the managers."
Kepa's moment of public insubordination at Wembley overshadowed an improved performance from Chelsea even in defeat on penalties to City, and they built on the positives on their return to Premier League action against Spurs.
Asked if Wednesday's win could be a turning point in a difficult season, Pedro replied: "I think so. We have played very well in the last two games, we were more solid, more compact and we created more chances.
"Against City we already played a great game. It was a pity that we did not have luck in front of goal. Today we did have that and this is the way to go.
"We have to keep playing like this against the top teams and against any team every week to try not to drop points and be in the top [four], because now it is our main goal."