The spectacular winner by Summerville, which ended Liverpool's 29-game undefeated streak in the Premier League in the presence of their home crowd, served as the latest nail in the coffin for Klopp's team on a day when they were once again far below their best.
Jesse Marsch, the American coach of Leeds, was relieved by the outcome, but Liverpool stole the show on a night when they once again mismanaged their tactics dreadfully.
It will be interesting to watch how Klopp motivates his squad following consecutive losses to Leeds and inferior Nottingham Forest, however this was a day when their flaws were once again on display.
When Joe Gomez attempted to pass the ball back to Alisson Becker, the Liverpool goalkeeper slipped, giving Rodrigo an easy tap-in opportunity as Leeds grabbed the advantage in the fourth minute.
It was a surprising error from Gomez, who this season has made his way back into the Liverpool team and continues to dish out significant missteps that have been a consistent problem for his team.
"The issue is that at the present we are unable to handle this type of game, "said Klopp.
"Without a doubt, that was a disappointment. I believed we started off pretty well before giving up a bizarre goal.
"For some reason, even though we got the equalizer, it didn't restore our feeling of safety. We had trouble keeping the game under control and lost far too many balls.
"The players made an effort, we had good possession and good chances, but if you try to protect the area around the second goal in this way when the score is 1-1, you ultimately leave everything open.
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"Individual performances make up every team performance. One flows into another. You could watch the entire game, but you couldn't have defended as well as we did on the second goal, which is why we lost. It would have been a point instead, and we would have continued. Now that we have nothing, everything feels entirely different.
In his Sky Sports interview, Klopp said with a hint of annoyance, "Maybe some players are overrated, Harvey (Elliott) has been excellent for us this season. He got out to a strong start, but he faltered.
"We only have three attackers remaining, and Thiago has been unwell. In attack, the same players always play. Fighting is what we must do; it is what we must do.
"We struggle with bringing our best to the field of play. From the start, we were having injury issues. Starting on the first day, players had to participate.
Because of our circumstances, we must take care of ourselves, therefore we will.
On Sky Sports, Liverpool star Jamie Carragher didn't hold back in indicating that his old team's recent drop in performance is now a major concern.
Carragher remarked, "What has gone horribly wrong with this club this season?
"On the strength of what they've accomplished over the last four to five years, particularly last season when they were within two games of winning four trophies. absolute shadows of who they are.
Klopp must be considering what else he can attempt at this point, including other squad combinations, formations, and substitutions, as this is a significant issue for Liverpool.
This marked the first time in 71 appearances that Virgil van Dijk was on the losing side with Liverpool at Anfield, and that fact alone demonstrates the seriousness of the problem currently affecting a squad that has been so successful over the previous five years.
Is Liverpool really in crisis? Or they are approaching it?
Leave a comment below on your opinion
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Liverpool story