Moreno, returning to his home city, gave away the free-kick and penalty that led to his former club's first and second goals, as Liverpool squandered a 3-0 half-time lead to take only a point away from the Ramon Sanchez Pizjuan.
The Reds face Premier League champions Chelsea at Anfield on Saturday, in what is likely to be another stern test of Moreno's defensive credentials.
Klopp could opt for James Milner at left-back - the England international replaced Moreno in the 63rd minute on Tuesday - but the manager maintains an unshaken belief in the Spaniard's abilities.
"I had a talk, of course, to Alberto and I am really happy about his shape, I am really happy about his performances," said Klopp, who confirmed Emre Can is a doubt to face Chelsea due to a muscular issue, while Adam Lallana and Joel Matip remain on the road to recovery.
"Yes, I know in this game it was obviously [not his best] and that's then really my responsibility. I could have done different things and obviously it was difficult in Seville with all the circumstances; everyone was talking to him like a family member. He left there but a lot of people are still there who he knows well.
"[If you lose] one, two or three per cent of concentration and come a little bit too late and that's how it started. My response would have been to think about the line-up or change or change earlier or whatever. It's not the player to blame, I am 100 per cent responsible for that.
"I told him I still trust him 100 per cent, so for me the game is over. How you concede the goals is not important anymore after the game, only for the analysis but not for anything else.
"We know how we came into the situations and that's what we have to change."