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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.
Both sides could claim to have been deserving winners in a classic free-flowing encounter full of goalscoring chances, remarkable saves and four disallowed goals.
Victory for high-flying West Ham lifted them above Juergen Klopp's side into third place in the table.
With four wins out of four, Juergen Klopp's side can now take their foot off the gas for the final two games of the group stage.
An 83rd minute penalty from Ashley Barnes, after he was brought down by goalkeeper Alisson Becker, decided the contest after Juergen Klopp's side failed to score for the fourth straight league match.