Carragher: Carling Cup glory cannot be one-off for Liverpool
Carragher stressed the Reds must build on the success - and not allow it to distract them from their other aims this season.
"We have achieved something but there are two more targets, one of which (the top four) has been made more difficult but other results (on 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."