The Reds conceded four goals for the first time in European competition, as Real piled on three second-half goals to claim a strange hold of the last-16 tie.
That all came after Darwin Nunez and Mohamed Salah had put Liverpool 2-0 up inside 15 minutes, only for Real to square the game up from two Vinicius Junior goals before half-time in a pulsating opening 45.
But Militao ghosted in unmarked from a Luka Modric free-kick to head home for 3-2 in the 47th minute as Los Blancos raced away with victory, scoring goals at will on the counter.
“I really thought the 3-2 had a massive impact, I saw that as well,” Klopp told reporters.
“The 2-1 and the 2-2 not so much my personal feeling was, ‘first goal, OK, bad defending but well done as well, the second was slapstick but get over it and play from there and then the third goal directly after half-time, we didn’t deal particularly well with that, that’s true.’
“We don’t want to concede goals but I think if we just think about the first half, everybody’s impression was, ‘Wow, that was a really good first half’ even when we conceded two.
“I really thought our people saw it exactly like that, they were outstanding tonight in a difficult game.
“The first half it was not too difficult to be positive but in the second half when it was difficult to stay positive, they were positive and I am thankful for that.”
Liverpool and Real both had nine shots each, with the Reds actually registering more expected goals but it wasnt to be.
To add injury to insult, Joe Gomez appeared to suffer an injury and was forced off in the second half.
“We will see,” Klopp said. “He showed a little bit a sign but then we just made a decision.
“Now we will see and he will get checked tomorrow.”