Klopp's men have a mountain of work to do in their quarter-final second leg on Tuesday, if they are to stay alive in the illustrious European competition.
Gareth Bale, Isco and Cristiano Ronaldo all got on the scoresheet at the Bernabeu, with some suspect defending costing Dortmund for the latter two goals.
And Klopp was furious his side now have a three-goal deficit, claiming they could have been much closer heading back to the Westfalenstadion.
"We practically assisted two of their goals ourselves," Klopp said.
"You can concede the first goal, that was a well-executed attack, but we made it too easy for their second and third goals.
"We didn't defend the way we wanted, we left too much room and weren't as compact as I would have liked.
"But we also have to understand that we played one of the best teams in the world today."
Klopp conceded his side remained aggressive as they hunted for a crucial away goal, but said they lacked a class finisher.
"We had a lot of chances to score and pushed forward until the final whistle. It definitely would have helped for the return leg," he said.
"We've certainly been in better positions than being 3-0 down. A 2-0 victory in front of our home crowd is always a possibility, but that won't be enough now since we didn't score.
"We lacked the final touch in our attacks.
"We had a lot of counter-attacks where we either missed the opportunity or the final ball was inaccurate. So if we are eliminated next week, it won't just be because of our defensive showing tonight."
Demanding a 3-0 result out of his team will not be Klopp's attitude towards the second 90 minutes, with the result not his first priority.
"I'm not going to make any type of promises for the return leg, but we want to play attractive football and win the game if possible," he said.
"And if we do manage to win, we will just have to wait and see by what margin. But I'm not going to stand here and say, 'We'll blow them away'."
