Liverpool manager Brendan Rodgers admitted former club Swansea fully deserved the 3-1 victory which ended his side's defence of the Capital One Cup.
The Reds were well off the pace in the first half and trailed to Chico Flores' 33rd-minute header. Even the introduction of Luis Suarez and Steven Gerrard at the interval could not prevent Swansea scoring a second on the counter-attack through Nathan Dyer and although Suarez pulled one back quickly Jonathan de Guzman scored an added-time breakaway.
"I thought the best team won. We were too slow, there was no tempo in the first half," admitted Rodgers, who left Swansea to take over from Kenny Dalglish at Anfield in June. "It is disappointing. You can only hurt if you are the better team and I thought they were the better team."
He added: "Swansea were bright and creative and were very good and it took the introduction of Luis and Steven to up the tempo in the second half. Then we looked like we could score and create chances but we couldn't get the goal.
"We got done on two breakaways but the best team won, that was clear. They took their chances very well. I am disappointed to be out of the competition but I don't think we can have any complaints."
Swansea boss Michael Laudrup, having succeeded Rodgers, hailed the club's achievement of reaching the quarter-finals of the competition for the first time.
"I think we deserved the win and it is not very often you can say that as a manager playing at Anfield against Liverpool," he said.
"To win at Anfield is great so maybe it is (the best performance of his short reign). For 80 minutes we played a really good game with some fantastic counter-attacks and it was nice to watch.
"It is the first time the club has gone so far in the competition and to be in the last eight is great.
" It is a great achievement for the squad and the fans and now we can enjoy it but not for too long because we have another big game at Chelsea."