The 34-year-old was part of the Liverpool side that beat Cardiff City on penalties in last year's final and Carragher has insisted that the club want to do all they can to win a trophy early on in the season.
Carragher told the Daily Mail: "We are the holders and don't want to give it away.
"Wembley was fantastic last season. This trophy is ours and we want to hold onto it.
"This is a quick-fire competition, and with the final being in February, you can achieve something very early. That's what we want to do."
Carragher is expected to feature when Liverpool host Swansea City on Wednesday night.