"[The League Cup is] very big because the fans and ourselves deserve a trophy because of all that we have done in the three years that Brendan Rodgers has been here [as manager]," Borini told the club's official website.
"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."
Liverpool travel to Newcastle United this Saturday.