Fulham won a penalty shootout after scores had finished 1-1 after extra-time.
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Castagne told the club's website: "It was a long game, we ran a lot, but a good result. It felt great (to win on penalties), Bernd did his job!
"We stayed in the game, we tried to score but in the end we finished it off.
"My performances have just been down to working hard. I kept fitness and had to stay ready to step up."
He added, "Obviously I've won this competion once before, so it would be an unbelievable feeling to win it here!"