Manager Michael Laudrup has urged Swansea to emulate his ex-team Getafe and be a "smaller club" to reach a major cup final and qualify for Europe.
Swansea reached the Capital One Cup quarter-final for the first time after Chico Flores, Nathan Dyer and Jonathan De Guzman scored to
beat Liverpool 3-1.
Championship side Middlesbrough will visit in the last eight as Laudrup's men target a first major cup final.
"The league is most important... but a cup run is fantastic," he said.
Only Arsenal and Premier League leaders Chelsea are both above Swansea in the league and remain in the league cup as Manchester United, Tottenham Hotspur and Sunderland as well as Liverpool exited the competition.
- Swansea have scored three goals in seven of their last 10 League Cup matches.
- The Swans' last cup game at Anfield was an FA Cup third round tie in January 1990 which they lost 8-0.
Swansea will host Middlesbrough in the week beginning 10 December as Laudrup, whose side are now two games from Wembley, hopes his new team can follow his old club's example in 2008.
"At Getafe it was the same," recalled Laudrup, a 1992 European Cup winner with Barcelona.
"They were a smaller club that just started to play the Spanish Cup and we went on and suddenly we were in the final, where we lost to Valencia.
"But to be a small club in the final, it is great. In that season at Getafe, it carried on in the Uefa Cup where we played Bayern Munich in the quarter-final.
"We also beat great teams like Benfica and Anderlecht in Europe. It was great.
"Bigger clubs are more used to making finals, it is different for smaller clubs. It is the first time this club has gone so far in this cup and it is the shortest way to play in a major final and have success.
"We all agree, and me included, that the league is always the most important because it is our daily bread. But a cup run is fantastic."
Swansea's 3-1 triumph at defending champions Liverpool, beating former boss Brendan Rodgers's new side, was only their second ever victory at Anfield.
Swansea's cup run
- Round 2:
Beat Barnsley 3-1 (a), 28 Aug
- Round 3:
Beat Crawley 3-2 (a), 25 Sept
- Round 4:
Liverpool 3-1 (a), 31 Oct
v Middlesbrough (h), 10/11 Dec
Laudrup succeeded Rodgers at the Liberty Stadium in June
after Rodgers left to take over from Kenny Dalglish at Liverpool.
"We played a great game and we deserved the win," said Laudrup.
"And to say that after playing at Anfield against Liverpool, there's not very often you say that as a manager.
"The name Liverpool and Anfield is so big, so it is a great achievement for the club winning here."
But Laudrup did have a warning for his players as Swansea prepare for leaders Chelsea's Premier League visit to the Liberty Stadium on Saturday.
"The club can enjoy this but the players not for so long as in 72 hours we have another important game in the league," Laudrup said.
Goal-scorer Chico was replaced by Garry Monk just before the hour at Liverpool with a dead leg and Laudrup, who is already without injured keeper Michel Vorm and left-back Neil Taylor, confirmed the Spanish centre-back is a doubt for the Chelsea game.