The Reds blew a three-goal lead, built by two goals from Roberto Firmino and one from Sadio Mane, and a chance to secure their place in the last 16 of the Champions League.
Wissam Ben Yedder scored twice in the second half before a 93rd-minute equaliser from Guido Pizarro earned the hosts a point.
Liverpool must now avoid defeat in their final Group E game against Spartak Moscow on December 6 at Anfield and only a win will ensure they go through as group winners.
Klopp said: “We stopped playing football in the second half. We have one real weapon – playing football – and we didn’t do that in the second half before we conceded the second goal.
“It was absolutely OK that we were confident after that first half. It’s obvious what we did – the real problem is we stopped playing football.
“Our main mistake was that for 15 minutes we didn’t play football, we were passive, we were a little bit too deep. They fought back and well done to them.
“We opened the door for them didn’t close it, they could score in the last minute.
“It feel like we lost but we didn’t lose. There is a game to go and it’s still in our hands but at the moment it feels really bad.”
Liverpool appeared to buckle under pressure in the second half as the hosts piled forward in a raucous atmosphere at the Estadio Ramon Sanchez Pizjuan. But Klopp claims it is not a mentality problem.
“The atmosphere helped Sevilla a lot,” he said. “They had to show character, they did and we let them back into the game.
“We showed already fantastic mentality in a lot of other games. Yes it was not perfect tonight but it’s not a general problem.
“We need to get more and more experience. Could we have done better? 100 per cent. It was misjudgment, we wanted to play like we played the first half. We became a little bit passive.”
Liverpool captain Jordan Henderson was visibly upset at the final whistle and said: “I’m not sure [how the collapse happened]. The first half was very good, disciplined, score good goals. The second half was very bad, we did not start well at all. We gave a corner away and struggled from then on.
“We stopped playing football and did not get the ball to the front three to cause them problems. it does not feel good.
“We did not keep the ball and I did think the free-kick and penalty decisions were soft to let them back in the game. We need to be better.
“The message at half-time was to keep going and they were going to give it a right go, they had nothing to lose and we could not cope with it. At least it is still in our hands to top the group.”