The coach was disappointed that his forwards could not convert their chances in the absence of Robert Lewandowski and suggested that could be their downfall
The Schwarzgelben were without star striker Robert Lewandowski due to suspension and the team's other attackers were unable to compensate for his absence at the Santiago Bernabeu.
Goals from Gareth Bale, Isco and Cristiano Ronaldo ruined the evening for the visitors and Klopp - who guided the team to the final last season, knocking out the Blancos in the last four - was left to rue missed opportunities and slack defending.
"We were not compact enough," the coach told Sky. "We stood deep and we stood wide, but we were not compact enough.
"Real always score at home. So when they do it does not matter with regards to the early goal. We could have scored five, but we did not.
"With the second and third Madrid goals, it is a fact that we had the ball both times but we gave it away cheaply.
"We ran a lot and we really fought for at least one goal but we did not get it. We certainly had better situations to get into a game and, if we go out next week, certainly some wasteful attacking from this match will be to blame.
"We will fight and give our everything again in the second leg."