Moreno was at fault for the two Yassim Ben Yedder goals that led Sevilla to recover from a 3-0 half time deficit and take a point.
The Spaniard, who joined Liverpool from Sevilla in 2014, conceded a cheap free-kick at the start of the second half then allowed Ben Yedder to ghost in at near post and score.
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Six minutes later, Moreno was penalised again after treading on Ben Yedder's foot in the penalty area and, after a re-take, the Frenchman converted the spot-kick past Loris Karius.
Klopp substituted Moreno shortly after and the full-back's performance was heavily criticised post-match, but the Liverpool manager claims full responsibility for his player's display.
When asked whether he was happy to 'allow' players to make mistakes, Klopp said: “It's not about allowing, it happens. I'm really used to that. That's how it is. You cannot change it, you have to deal with it. In this world especially.
“In this case, I had a talk with Alberto and I'm really happy about his shape, I'm really happy about his performances. It was really my responsibility.
Klopp added: “In Sevilla, everyone was talking to him like they were talking to a family member. He left there, a lot of people are still there that he knows well. You lose one, two, three per cent of concentration over there, you come a little too late and that's how it started. That's how it is.”
Moreno suffered in a similar fashion during the 2016 Europa League final against Sevilla, when the Andalusian club staged a similar second-half turnaround to win 3-1.
After that performance, Moreno's Anfield career was essentially postponed, with makeshift left-back James Milner replacing him in Klopp's starting line-up for the majority of the following campaign.
At the start of this season, however, Milner has returned to midfield and Moreno has fought off competition from new signing Andy Robertson to make the left-back berth his own.
Klopp suggested that despite Moreno's errors in Seville, he has no plans to take him out of the firing line again, insisting that the 25-year-old still has his trust and support.
“It's not a player to blame, I am 100 per cent responsible for that,” Klopp said. “I told him I still trust him 100 per cent.
“For me, the game's over. How you concede the goal is important for the analysis but not for anything else. We know how we came in the situation and that's what we have to change.”
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