The Reds' number seven was left out of the squad for the Premier League clash, after his parents were kidnapped in his native Colombia.
Local media reports reported that Diaz's parents were taken by armed men on motorbikes in their home town of Barrancas on Saturday.
While Diaz's mother, Cilenis Marulanda, was found safe on Sunday, his father, Luis Manuel Diaz, remains missing.
The national police are offering a reward of around £40,000 for information, while Colombia President Gustavo Petro has said that 'all the public forces have been deployed' to find Diaz's father.
Speaking in his post-match press conference after Sunday's victory, Klopp revealed when he and the squad first learned of the situation.
“We heard about it late last [Satruday] night,” the manager said. “We spoke to Lucho, he wanted to go home, we sent people with him, have people there who take care [of him].
“There are parts of his family there as well, that’s why they want to be together, that’s absolutely understandable.
“We got the news with the mum, which is fantastic, and since then nothing really. They all work on it, clearly.
“It’s quite some distance and we are obviously not the first people who get informed, but we try to get knowledge of everything as much as we can.
“But we don’t want to disturb in any way. We are not the important people there, we just want to support. That’s it.”
— Liverpool FC (@LFC) October 29, 2023
Klopp added that the distressing incident made focussing on the game 'impossible', while Diogo Jota's goal celebration – during which he held aloft a 'Diaz 7' shirt – was 'touching' and 'wonderful'.
“How can you make a football game really important on a day like this? It’s really difficult,” Klopp said. “I never struggled with that in my life, it was always my safe place, sometimes my hiding place.
“As a player, as a coach, you are allowed in these 90-odd minutes to focus just on that. And it was impossible, absolutely impossible to do that.
“It was clear we have to give the game an extra sense, and that was fighting for Lucho.
“Then the boys pulled out the shirt and I was not 100 percent prepared for that, to be honest. It was really touching, but wonderful as well.”