Caballero is confident the players want to match the history of the club.
The Argentine told the Chelsea website: "Chelsea is an important club, a big, big club. You see that in America, in South America, everywhere.
"The supporters are across the world and their ambition is always there. So it’s on us to defend the name and the colours.
"We have to match the history and, as a staff, help create a great team that can compete. We have done this with qualifying for the Champions League and winning the Conference League, but we have to keep going."
What sets Maresca apart
Caballero also said: "I’ve been very fortunate in my career – in the Premier League and other countries – that I have worked with many top coaches.
"But I don’t think anyone is as well prepared, tactically focused, and trains the details to give solutions to the players like Enzo (Maresca).
"I felt this very quickly. In the moment I decided to finish my playing career, he had a space for me on his staff and I saw how he coached, managed the moments in the week and how he can interpret the game.
"He is also good at making you feel important. He gives us moments or time in the week or during a game where you speak with the players and help the players. So I believe he is a top manager."