The Argentinian - whose place in the side was questioned by many ahead of the match - saved from Philippe Coutinho, Lucas and Adam Lallana as City won the spot-kicks 3-1 to land the first piece of silverware of the season.
The game finished 1-1 after extra time after Coutinho had equalised Fernandinho’s goal.
Caballero said: “It’s amazing, we won this cup, for me it’s amazing. It was a hard, hard week for me. We have the trophy now – it’s fantastic for the Blue people.
“It’s emotional for me, for my family – this is for sure for me, for all my people, for my family in Argentina.”
On how he produced such a phenomenal shoot-out performance, Caballero added: “Just intuition – I tried to watch all the penalties last night but my intuition helped me.
“He [Pellegrini] gave me the opportunity to come here and play for this club in this final.”
Striker Sergio Aguero - who scored his penalty along with Jesus Navas and Yaya Toure - added: “It’s fantastic for Willy – I’m happy for him because he played every game and I’m happy with him.”
