A brace from Andre Ayew and a goal from Jack Cork did the trick for Francesco Guidolin’s side, who gave the Reds a glimmer of hope when failing to pick up Christian Benteke from Sheyi Ojo’s 65th-minute corner.
However, two minutes later, Ayew bagged his second to leave Liverpool without a win in their last three games of league and cup football.
To make matters worse, they had Brad Smith sent off for a second yellow card 15 minutes from time.
“I tried to freshen up the side because we have had three games in a week,” said Klopp.
“However, we didn’t play that well today. It doesn’t mean that I have changed my opinion on the young players who played against Bournemouth and here today.
“As I say, we just didn’t play as well as we could.
“Had we played close to our best today, it would have been a far closer game. But we didn’t.
“The Europa League now becomes our focus, but after Thursday, the Premier League will once again be our focus. As I say, I am disappointed, but we will prepare for the second leg and see what happens.
“Maybe the performance was influenced by the number of games, but I want to influence the number of games we have in the future.
“Ten days ago we were in brilliant shape, now it is not so good shape. But it is one game and we are developing well.”
Swansea broke the deadlock in the 21st minute courtesy of Ayew.
A sweeping move, from deep, led to a corner on the left and when Gylfi Sigurdsson whipped in a teasing cross, Ayew rose to head home from point-blank range.
It was the Ghanaian’s first goal since January.
It could have been two, five minutes later, had it not have been for Liverpool goalkeeper Danny Ward. Neil Taylor’s precise cross was met by Cork, who saw his goal-bound shot kicked to safety by the diving Ward.
There was nothing Ward or any one of the Liverpool defenders could do about Cork’s 33rd-minute strike from 25 yards.
The former Southampton midfielder nicked the ball in midfield and after closing in on the 18-yard box, he beat Ward with a wonderful effort.
With a greater percentage of possession after the break and with Lucas and Benteke having replaced Coutinho and the ineffective Pedro Chirivella, the visitors looked increasingly dangerous.
Lucas provided greater stability in the central area with Benteke working well alongside Sturridge.
Their desire and ambition almost brought its reward on the hour when Nathaniel Clyne found himself inside the penalty area with only Lukasz Fabianski to beat.
However, the Polish keeper was equal to the threat and with the help of Taylor, scrambled the ball clear.
From the ensuing corner, the visitors were back in the game.
Ojo’s delivery was inch perfect and Benteke beat Fabianski with a firm header.
Liverpool’s joy turned to despair two minutes later. Jefferson Montero led the Liverpool back four a merry dance before finding Ayew in the box. He held off all comers and duly found the bottom corner from 12 yards.
Any hopes Liverpool might have had of a comeback disappeared 14 minutes from time with Smith’s departure.
Swansea might have added to their tally in the final 10 minutes, but Ayew and Cork were both denied by some desperate Liverpool defending.
With the mathematics now ensuring his first spell in the Premier League has been a success, Guidolin said: “I felt we were safe a few weeks ago, without being mathematically safe.
“I am also satisfied with the way we responded after the defeat in Leicester.
“I thought we were very good today and I’m happy that we have won. We have two games to go and I am proud of the job I have done since coming in.”
Fabianski 6; Rangel 7, Amat 7, Williams 7, Taylor 7; Cork 8, Britton 7 (Fulton 90,5); Montero 7 (Naughton 72,6), Sigurdsson 7, Routledge 7; Ayew 8
Nordfelt, Ki Sung-Yeung, Gomis, Fernandez, Fulton, Barrow
Ward 6; Clyne 6, Lovren 6, Skrtel 6, Smith 5; Chirivella 4 (Lucas 45, 6), Stewart 6; Ojo 6, Coutinho 6 (Benteke 45, 6), Ibe 6 (Brannagan 80,5); Sturridge 6
Mignolet, Lallana, Teixeira