Diaz was not involved in the Reds’ Premier League clash on Sunday, after worrying developments in his native country of Colombia.
The winger’s parents were kidnapped in the town of Barrancas on Saturday night, with his mother subsequently rescued but his father still yet to have been found.
Liverpool confirmed the absence of Diaz for their 10th league game of the campaign an hour before kickoff, with Jota starting in his place.
The Portuguese went on to open the scoring in the 31st minute at Anfield, before an emotional tribute to his team-mate.
Jota wheeled away towards the Liverpool dugout before holding aloft Diaz’s No. 7 shirt, then being joined in a fitting celebration.
Speaking before kickoff, Klopp explained the decision to grant Diaz compassionate leave, expressing concern for the player and his family after a “really tough night.”
“We had to obviously make a late change because of the private situation involving Luis Diaz,” Klopp told BBC Sport.
“It’s a worrying situation for all of us and it was a pretty tough night.
“I have never had that before. It’s a new experience I never needed.”
Darwin Nunez went on to put the Reds 2-0 up before half-time at Anfield, with Liverpool dominant and enjoying 74 percent of possession.