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The Dutchman was in charge of Eredivisie side Feyenoord.
Strikes from Mohamed Salah, Andy Robertson, Cody Gakpo and Harvey Elliott earned the victory for Klopp's men, who had won one of their previous five league games and seen their title challenge crumble.
Salah seemed to have a different perspective and refused interviews with reporters in the mixed zone, saying: 'There's going to be fire today if I speak.'
The German joined Liverpool in October, 2015, and has won the Champions League, Premier League, Club World Cup, FA Cup, League Cup and Super Cup, as well as the Community Shield during his time in charge.
Liverpool forward Diogo Jota held up Diaz's No. 7 shirt to show support for him after scoring the first goal of the match as the 2019-20 champions stayed fourth in the table with 23 points from 10 games.
The Italian side were magnificent in the opening 45 minutes, going in 3-0 up at the break having opened up a woeful Liverpool defence at will.
The match ended goalless with both sides hitting the woodwork.
Pep Guardiola's City bounced back from 0-2 to win 3-2 against Aston Villa.
The Reds hung on to beat Manchester City 3-2 at Wembley Stadium to reach the final of the FA Cup.
Liverpool equalised twice in the 2-2 draw as the two sides remain separated by just a point in the table.
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