"It's not been an easy week for him but his behaviour is fantastic," Caballero, who started his third successive match in Sunday's 2-1 home win over Swansea, told British media.
"He supports me and we are working really hard and he has a competitive mind, so he's doing very well.
"Claudio is a fantastic player, a fantastic keeper and we have to respect him because he is probably the keeper with more titles in his country in the last two years."
Caballero said he was relishing being City's first-choice keeper, no matter how long it might last.
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"I was always waiting for the cup but now I am ready for every single game. The boss (Pep Guardiola) took a decision and I try to enjoy every single day," he said.
"I accepted it immediately, I loved it immediately and I tried to do my best during the game. I will try to work really hard for the rest of the week, but he always makes the decisions for the team."
City, who are third in the Premier League, 10 points behind leaders Chelsea after 24 games, travel to face 14th-placed Bournemouth on Monday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Robin Pomeroy)
