The victory over Cardiff on penalties at Wembley sealed the club's first trophy for six years.
But with an FA Cup quarter-final coming up next month and the race for the top four hotting up, the 33-year-old knows they cannot afford for a record eighth League Cup to dilute their ambition, even if it means they have already qualified for the Europa League.
"We have achieved something but there are two more targets, one of which (the top four) has been made more difficult but other results today [Sunday]," he said, referring to Arsenal's win over Tottenham.
"But we're still in the FA Cup and we want to come back here again, whether that be a semi-final or a final.
"It would be great to go on and do well in the FA Cup, that is what we want to do."
Carragher was asked whether manager Kenny Dalglish, who tried to keep his emotions in check, had enjoyed winning his first piece of silverware for Liverpool since the 1990 league title.
"I am sure it means a lot to him," he added.
"This season has a long way to go, but inside I am sure he is delighted."
Defender Daniel Agger was pleased the club were able to end their trophy drought.
"It was nice to win. It is a long time (without winning a trophy)," said the Denmark international.
"This is what it is all about, it is what we work for every single day.
"It is always sweet, I don't think you can say it is extra-sweet.
"We are still in the FA Cup, we are pushing in the league as well.
"It is football isn't it? So we have to believe and we still have that and now we have done it we have to push on.
"Every single game is important from now until the end of the season, there is so much to win.
"We still have fourth place to fight for and there are so many big games coming up."
Agger said their confidence never wavered throughout the game, even after going behind and then conceding an equaliser seconds from the end of extra-time.
"We created chances and we believed we could score," he added.
"Anything can happen in penalties but we've been in that situation a few times before."