The dramatic penalty shootout victory over Cardiff at Wembley on Sunday ended Liverpool’s six-year wait for silverware.
Speaking to Drive Time, Carragher said: “It has been too long. We’re coming to the latter stages of our career myself and Stevie [Gerrard] and because we have gone so long without winning anything you don’t want to finish your career going seven or eight years without.
"It was a relief for both of us to get a trophy, for ourselves and the club. It maybe takes the pressure off now for the next year or two and we can maybe relax and go on to try and win more trophies, hopefully bigger trophies.
“The Carling Cup, even though we are delighted to get it, it’s probably the one out of the four that’s maybe not the biggest out of the rest of them. We’re delighted to get it but hopefully we can go on to bigger and better things this season and hopefully next season as well.”
Sunday’s final was the first Wembley appearance for Carragher in Liverpool colours and the 34-year-old has targeted a return to the famous arena this season, with the FA Cup now in his sights.
“It was a big day for everyone,” he added. “A lot of players it was their first big game and first trophy, which is great, but even for people like me and Stevie to play at Wembley for Liverpool was always something we dreamt of doing.
"Thankfully we’ve done it now and we have got a trophy as well and hopefully we can go there again sometime this season.”