The Premier League side looked set to qualify for the knockout stages when they cruised into a commanding advantage, Roberto Firmino's brace of goals sandwiching a diving header from Sadio Mane.
However, Liverpool collapsed after the break at the Ramon Sanchez Pizjuan, Wissam Ben Yedder scoring twice before Guido Pizarro grabbed an injury-time equaliser for the hosts.
Alberto Moreno endured a nightmare return to his old club, giving away a free-kick and a penalty that led to goals, though Klopp refused to lay the blame entirely at the feet of the Spanish left-back.
3 - Liverpool have 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). Comeback.— OptaJoe (@OptaJoe) November 21, 2017
"It's obvious, we played a very good first half and we stopped playing football in the second half," he told BT Sport.
"We didn't play until we conceded the second goal, after that we improved and had a couple of chances, but they got the equaliser.
"When you're the winning team you should avoid this first of all, it was absolutely OK that we were confident after that first half.
"Then we were in two situations too late, not only Alberto but the whole formation. They had the free-kick and then the penalty. But the real problem is that we stopped playing football.
"We could've closed the game. Our main mistake was that we didn't play football anymore. We got passive and a little too deep."
"They fought back, so big credit to them, but we have to do it differently," Klopp added.
"It feels like we lost, but we didn't. There are two games to go [in the group] and it's still in our own hands. For now, though, it feels really bad.