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The Premier League champions had their incredible unbeaten home league run stopped on Thursday, as Sean Dyche's side shocked their hosts, losing their first game at Anfield since 2017.
Ashley Barnes' penalty, won after goalkeeper Alisson felled the Burnley forward, was the only difference between the two sides but Klopp blamed himself for his side's failure to score for a fourth league game in-a-row.
The German wasn't the only one who laid the blame at his door, with one particularly disgruntled fan calling talkSPORT to complain about the former Borussia Dortmund manager.
David, suspiciously lacking a scouse accent, thinks the manager has taken the team as far as it will go and his lack of a plan B will stop him winning any more trophies in Merseyside.
:rage: "Klopp has taken #LFC as far as he can. He's taking them backwards!"- talkSPORT (@talkSPORT) January 21, 2021
:x: "He has got no plan B. They should go for Allegri or Simeone."
:angry: "I don't think Klopp will win anymore trophies at Liverpool."
This Liverpool fan thinks it's time for a Klopp to leave the club... pic.twitter.com/oVjM1j7lN3
The caller acknowledged the fact the 53-year-old had won both the Champions League and Premier League during his spell at the club, the latter just seven months ago, but that isn't enough for him.
He also recalled calling previously, 'a few years ago' to say the manager should go, presumably before he'd won the two elite competitions, as well as the World Club Cup and UEFA Super Cup, so he'd admitting his own previous failing.
Burnley lead the champions at Anfield! :flushed:- Sky Sports Premier League (@SkySportsPL) January 21, 2021
Ashley Barnes hits the deck in the penalty area and Mike Dean points to the spot - do you agree with the decision?
Watch live on Sky Sports PL :tv:
Follow #LIVBUR online here :calling: https://t.co/7HtKtrdULt pic.twitter.com/B5RmPP3gSg
Liverpool beat Crystal Palace 7-0 on December 19th but have only scored once in the five league games since then, scoring four in the FA Cup third round against Aston Villa.
There only strike in the Premier League in that run came against West Brom, in a 1-1 draw with Sam Allardyce's side, and they have won just three points in that time.
The defending champions have dropped to fourth in the league, six points behind leaders Manchester United, with Spurs and Everton able to go above them, should they win their games in hand.
The Reds have had quite a few injury problems this season, with Virgil van Dijk being the most high profile, but their biggest loss right now is probably Diogo Jota, with the former Wolves player scoring five goals in nine appearances before his injury.
No matter what happens between now and the end of the season, you can't help but feel that, despite David's annoyance, there's no chance Klopp will lose his job.
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