Liverpool made it five games without a defeat when they defeated Forest 3-0 at Anfield on Sunday, with Diogo Jota, Darwin Nunez and Mohamed Salah scoring.
The game came just hours after it was confirmed that winger Luis Diaz's parents were kidnapped in Colombia this weekend.
The player's parents were stopped by men on a motorcycle and taken away. While his mother was released hours later, police are still trying to rescue his father and have offered a significant reward for information that will lead to his release.
The 26-year-old was left out of the squad for Sunday's match and his replacement, Diogo Jota, held up his team-mate's jersey in a show of support after scoring Liverpool's first goal. The Portuguese attacker then spoke about the situation after the game, deeming it "unimaginable".
Klopp hopes that his team's success against Forest will provide an upbeat distraction for the player, but admitted the circumstances were terrible for his team.
He said to Sky Sports: "We played in the most difficult circumstance I've ever had. It was a really difficult day, which ended with a good result.
"The best thing we could do for our brother was that, we win the game and distract him a little bit maybe, all the rest was super special in the most negative understanding. After more than 1,000 games you would think you have experienced everything, but no.
"But it's not about us, it's about 'Lucho' and his family, and we all pray and hope that everything will be fine. What we can do, we will do, we've done already in the club and the only thing we could do today was fight for their brother - and that's what they did."
Klopp added in his press conference that he spoke to the Colombia star, revealing that he wanted to go home after receiving the news.
"The preparation was the most difficult I ever had in my life," he said. "Didn't expect that, was not prepared for it, I don't want to make the game bigger than it was, but it was definitely,. We tried to help Lucho with the fight we put in because obviously, we want to help, but we cannot really help, so the only thing we can do is fight for him and that's what the boys did.
"We heard last night late about it. Then we spoke to Lucho; [he] wanted to go home, [we] sent people with him, have people there who take care, there's part of families there as well so that's why they want to be together. Absolutely understandable.
"Then we got the news with [his] mum, which is fantastic, and since then nothing really. They work on it, clearly. By some distance, we are obviously not the first people who get informed but we try to have knowledge of everything as much as we can, but we don't want to disturb in any way. [We're] not the important people there. We just want to support [the family]. That's it."
He continued: "So how can you make a football game really important on a day like this? It's really difficult. I never struggled with that in my life. It was always my safe place, sometimes my hiding, as a player or as a coach, you are allowed during these 90 minutes just to focus on that and it was impossible. Absolutely impossible to do that. It was clear we had to give the game an extra sense and it was fighting for Lucho, then the boys put out the shirt and I was not 100 per cent prepared for that, to be honest. It was really touching but wonderful as well. So, yeah, that's it."