The Reds looked to be coasting into the knockout stage for the first time since 2009 as two goals from Roberto Firmino and one from Sadio Mane put them in total control.
Yet after Alberto Moreno needlessly conceded a free-kick against his former club, Wissam Ben Yedder's header made it 3-1.
Moreno then conceded a penalty by clipping Ben Yedder, and the French striker scored after being ordered to retake a successful spot-kick because of encroachment.
Guido Pizarro poked home in the third minute of added time as the hosts snatched a draw.
"I don't doubt the mentality of the boys, not a bit," said Klopp, whose side must avoid defeat when they host Spartak Moscow on 6 December to ensure they advance from Group E.
"We showed already a fantastic mentality. We showed it in a lot of other games. It's not like this.
"Yes, it was not perfect, that's true, but it's not a general problem.
"Could we have done better? 100%. Do I think it's a mentality problem? 100% not. It's a misjudgement."
A first half to remember
When the half-time whistle blew, five-time winners Liverpool looked set to join Premier League rivals Manchester City and Tottenham in the draw for the last 16 on 11 December.
The Estadio Ramon Sanchez Pizjuan has become a fortress for Sevilla, with no visiting team having won there for more than a year.
Yet the Spanish side were stunned as Liverpool, inspired by Philippe Coutinho, produced a scintillating first-half display.
Coutinho corners led to the first two goals.
The first, with 88 seconds on the clock, was flicked on by Georginio Wijnaldum into the path of the unmarked Firmino, who swept home for Liverpool's second fastest goal in the competition.
Firmino then turned provider as he flicked on another corner for Mane to power home with his head, his first goal for the Reds since 27 August.
Moments earlier, Sevilla had two chances to equalise - Reds keeper Loris Karius using his left hand to save from Nolito before Ben Yedder fired wide when he should have scored.
But the game looked to be over when Firmino tapped home to make it 3-0 on the half-hour, Mane's shot parried into the Brazilian's path for a simple finish.
A second half to forget
Liverpool famously came from 3-0 behind to beat AC Milan in the 2005 final, but here they were on the receiving end.
Sevilla's comeback started in the 51st minute, Moreno conceding a foul which allowed Ever Banega to whip in a free-kick which Ben Yedder glanced home.
Moreno's night went from bad to worse nine minutes later.
The full-back failed to control the ball inside his own area and ended up fouling Ben Yedder, who beat Karius for a second time from the spot after German referee Felix Brych ordered a retake.
Liverpool had become a mess at the back.
Substitute Franco Vazquez fired straight at Karius before the Reds keeper got his hand to Sergio Escudero's fierce strike, the ball hitting the underside of the bar before rebounding to safety.
Their reprieve was short-lived, though, and Pizarro struck in the dying moments after the visitors failed to deal with a corner to leave Liverpool with work to do.
"Too many Liverpool players in that second half, they looked as if they felt the game had been won and stopped playing," former Chelsea winger Pat Nevin told BBC Radio 5 live.
"Jurgen Klopp must be devastated, he was seconds away from getting out of the group stage.
"Sevilla deserved their point, they were far the better side in the second half. Having said that, in the first half Liverpool were light years ahead."
Defensive frailty resurfaces
Liverpool arrived in Spain having kept three clean sheets in their previous four games.
But they have now conceded 28 goals in 20 competitive games this season, and let in three or more four times.
Questions must once again be asked about their defensive frailty.
Moreno, in particular, had a night to forget on his return to the club he played for from 2012-14.
Man of the match - Roberto Firmino (Liverpool)
Been here before - the stats
- Liverpool let a three-goal lead slip in a competitive match for the first time since May 2014, against Crystal Palace in the Premier League (also 3-3).
- The Reds have scored the same number of goals in their past three Champions League games (13) as they did in their previous 14 combined.
- In the two games between these sides in the Champions League this season, Liverpool have attempted more than twice as many shots as Sevilla (37 v 18) but scored the same number of goals (five).
- This result means Premier League clubs are unbeaten in six successive Champions League matches against teams from La Liga (W2 D4 L0).
- Firmino has been involved in seven goals in five Champions League appearances this season for Liverpool (five goals, two assists).
Liverpool need to rediscover their defensive solidity as they turn their attention back to the Premier League and a visit from champions Chelsea on Saturday (17:30 GMT).