There are few more damning indictments of a club on a downward spiral than a caretaker manager accusing his team of being unprofessional. Leon Britton took that drastic step at Anfield and no one representing Swansea City could complain. No fight, no heart and precious little quality; this was a performance that deserved damnation.

Liverpool were irrepressible in the second half with Philippe Coutinho orchestrating a rout, Roberto Firmino scoring twice and Mohamed Salah cutting at Swansea’s fragile confidence as Jürgen Klopp’s team made it 12 goals in three league games. The extent of the visitors’ collapse was embarrassing, however. Huw Jenkins, the Swansea chairman, slumped lower and lower in his padded seat in the Anfield directors’ box as the goals rained down and the importance of appointing a miracle-worker to succeed Paul Clement became increasingly apparent.

Swansea have spent the past three Christmases in the relegation zone but their prospects of repeating previous escapes to 12th and 15th in the Premier League appear non‑existent on current form.

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Britton has made it clear he is not interested in the Swansea job on a full‑time basis at present and given the error‑strewn display at Anfield, where Jordan Ayew and Leroy Fer resembled bystanders to the onslaught, it is no wonder.

“The first half was not too bad after going a goal down and the players grew in confidence,” said the midfielder, who expects to remain in charge for the trip to Watford on Saturday. “But after we conceded the second goal all belief and confidence drained from the players.

“We made a lot of basic errors – setting up at set pieces, clearances, misplaced passes – and when you make those mistakes against a team of Liverpool’s quality you’ve no chance.

“They were basic errors you expect to see at academy level,” Britton said. “At the same time, even when you are in a difficult situation you have to remain focused, stay professional and do the right things. I have to be honest, I didn’t see that from all the players.”

Liverpool appeared set for a comfortable home win as soon as Coutinho gave them the lead with six minutes gone. Several Liverpool goals stemmed from errors by the visitors and the breakthrough set the tone, with Ayew tumbling too easily under pressure from Firmino to concede possession cheaply inside the Swansea half. His team paid a swift and heavy price.

Facebook Twitter Pinterest Roberto Firmino, right, celebrates his first and Liverpool’s second with Philippe Coutinho, who scored the opener. Photograph: John Powell/Liverpool FC via Getty Images

Firmino sprayed the ball out wide to Salah, who switched the play immediately with a first-time pass to Coutinho on the left. Liverpool’s captain for the day had several Swansea defenders for company but a player of his talent requires just the fraction of space to make a difference. From 20 yards he curled an exquisite finish around his marker and just inside Lukasz Fabianski’s left‑hand post. The Swansea goalkeeper barely moved, such was the power and precision of Coutinho’s 12th goal of the season.

The expected procession towards victory did not materialise until after the interval. Klopp claimed: “Our timing was not good and our formation not good in the first half so we were always a bit too late and that allowed Swansea to play. But even then we had enough chances to have scored two or three goals.”

Once Liverpool emerged for the second half with greater urgency and aggression, however, Swansea simply wilted and the contest was quickly over. Coutinho supplied the second with a free-kick that caused a collective seizure in the Swansea rearguard. Firmino pulled away from Federico Fernández as the ball sailed towards the back post. Ayew stood and watched the danger unfold, not for the only time in the game, and Liverpool’s No9 guided a simple volley home from close range.

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Another Coutinho free-kick, cleverly cut square behind a crowded penalty area, almost presented Salah with the third but Liverpool did not have to wait long to extend their lead. The Brazilian was again involved, releasing Andrew Robertson on the left after an intricate show of skill, and one full-back assisted the other as the Scot’s cross was headed out to Trent Alexander-Arnold by Alfie Mawson. The header could have been won by Ayew but Alexander-Arnold wanted it more and beat the dawdling midfielder before driving an unstoppable finish in off the underside of Fabianski’s bar.

The fourth goal arrived within two minutes following an appalling mistake by the dreadful Fer. Mawson attempted to break out of his own half and found Fer, who responded with a pass backwards and straight to Salah. The Egypt international sprinted clear after that invitation and squared for Firmino to tap into an unguarded Swansea goal.

The rout was completed by Alex Oxlade-Chamberlain after Ayew, predictably by now, failed to react to the threat inside his own penalty area. Oxlade‑Chamberlain beat the winger once to play the ball out to Alexander-Arnold, and for a second time when the defender’s cross rebounded off Martin Olsson. The former Arsenal midfielder controlled the loose ball expertly before lofting a lovely finish over Fabianski and into the far corner of a battered Swansea goal.