The Reds had to come from behind to beat the Swans 2-1 with late strikes from Mario Balotelli and Dejan Lovren, and the veteran defender says it is a competition the side wants to win.
He told the Liverpool Echo: “The Capital One Cup is very important for the club. We want to play well and we want to win the competition.
“We’re not dreaming of Wembley, we’ll just take it game by game, give 100% and see how far we can go.
“But Liverpool want to win a trophy definitely and this would be a good one for us.”
The Reds are in their third season under manager Brendan Rodgers and despite coming so close to winning their first title since 1990 last term, and qualifying for this season's Champions League, the Northern Irishman has yet to win his first major trophy at the club - something which he has said time and again that he is keen to do.
Fabio Borini, who had a rare start for the Reds and played a crucial role in last nights game, told the club's website they are keen to win something for the fans this season.
"It's very big because the fans and ourselves deserve a trophy because of all that we have done in the three years that Brendan has been here.
"I think we really need to push into the final steps [of the competition]. The wins always give confidence, but the way we play football is probably the most positive thing.
"We showed today that we are a very strong team, mentally, because we kept playing the way that we had started. At the end, we got the prize and we are so happy for the result and to go on to the quarter-finals."
Holders Manchester City and Premier League leaders Chelsea will be tough competitors to face, whilst Tottenham are also likely to be stern contenders in the latter stages of the competition.
If you want to win the competition, the chances are you have to beat the best teams at some stage, but a bit of luck with the draw would not go amiss for the Reds.