The Blues were beaten on penalties by Manchester City at Wembley on Sunday, having held their rivals to a goalless draw after normal and extra time.
Despite a resilient performance with plenty of positives for Sarri to draw on, Kepa's refusal to leave the pitch as a substitute for Willy Caballero overshadowed the team's exploits.
The Blues boss reacted furiously after the Spaniard's defiance and almost stormed down the tunnel before reluctantly allowing him to continue between the sticks.
Chelsea's final defeat marked their fourth reverse in five domestic games, with pressure mounting on Sarri as his tactics continue to be called into question by fans and pundits.
Hazard, who produced a star turn as a false nine against City and has been a talismanic figure for Chelsea throughout the 2018-19 campaign, says that the squad are still united under Sarri despite their poor run of results.
"We are all together," Hazard told Chelsea's official website. "We are all with the manager. I know this month was a bit hard but we need to be together, stay together, if we want to do something at the end of the season.
"At the moment we have a bit of pressure because the fans want us to be in the top four, but we’re Chelsea and we can deal with the pressure. We will win games and that’s it.
"We are there. This is a hard game but we can close the gap a bit on Tottenham. We have the potential to be in the top four but we don’t have to think about that. We just have to think game after game and try to win one more game.
"We are playing for him [Sarri], the club, the fans and us. It’s not just about the manager. He puts the players on the pitch and then it’s down to the players to take responsibility. On Sunday we played a fantastic game, we need to look at that and try to repeat it. Then the manager will be happy."
The Blues will be hoping to bounce back against Spurs in front of their own fans, in the fourth meeting between the two sides this season.
Spurs inflicted Sarri's first defeat as Chelsea boss back in November and they are still harbouring hopes of lifting the Premier League title, while their opponents chase the coveted final Champions League spot.
Gonzalo Higuain is expected to be restored to the starting line-up for Chelsea on Wednesday and Hazard went on to praise the club's January signing for his immediate impact at the club, while also discussing Olivier Giroud's value to the team.
"He [Higuain] is a top striker," Hazard added. "If we talk about how many goals he’s scored, he’s only got two with Chelsea, but you can see around the training ground he’s very intelligent. He’s not talking English a lot but he’s talking to the Spanish guys and Italian guys, and he also knows how the manager wants to play, so for us it’s great to have him in the team.
"I always say I need a great striker. When Olivier is playing it’s important for me, when Gonzalo is playing it’s important for me. What I want is for them to score goals, that’s it.
"We have a lot of intensity and when we have the ball we try to be in control of the game. I know the fans want us to go forward and try to find space between the lines but we try.
"Sometimes we play against compact teams so it’s hard to find solutions. I like the football we are trying to play, with and without the ball, so it can still be a good season."