The Reds were not at their very best at the Stadio San Paolo as they ended up losing to the Serie A side in their second group game this season.
Liverpool FC looked to be heading towards a point in the game, but Lorenzo Insigne poked home a dramatic winner in the 90th minute to claim all three points for the home side.
In truth, Napoli had dominated proceedings, with Dries Mertens hitting the crossbar in the second half.
However, the late goal will have come as a bitter blow to the Reds, who looked like they would be able to claim a point despite not being at their best.
The result left Group C wide open, with Liverpool FC second behind Napoli and PSG level on points with the Reds after two games.
And Klopp openly criticised both Mane and Firmino for taking too long in possession during Wednesday’s clash.
Speaking at his post-match news conference on Wednesday night, Klopp said: “The formation was not right, we moved in the wrong spaces, for the three midfielders the job was nearly impossible.
“With the ball we were to hectic when there was no reason to be hectic.
“Sometimes Bobby [Firmino] ran too long with the ball, or Sadio [Mane] ran too long. When that happens, you cannot produce.
“The midfielders or the full-backs tried to go forward, but we lost the ball and had to go back in the other direction.
“It was intense, but we caused the intensity of the game ourselves.”
The result left Liverpool FC without a win in three games as they now turn their attentions towards their top of the table clash with Manchester City at Anfield on Sunday afternoon.
The Reds are aiming to be one of the main contenders for the title this season, and a positive result against Pep Guardiola’s men will underline that status heading into the international break.
Liverpool FC have so far won six and drawn one of their opening seven Premier League games as they look to try and win their first major trophy since Klopp’s appointment at Anfield back in 2015.
Manchester City, meanwhile, warmed up for their clash against Liverpool FC on Sunday with a 2-1 defeat by German side Hoffenheim in their Champions League clash on Tuesday night.
The Citizens are currently top of the Premier League table on goal difference – but level on points with second-placed Liverpool FC.
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