After seeing the Blancos hammer Schalke in the last 16, the BVB boss is worried that his side could be swept aside at the Santiago Bernabeu, claiming that he is no "magician"
The Schwarzgelben edged Jose Mourinho's men out of the tournament in the semi-final stage last season, winning 4-3 on aggregate after surviving a second-leg onslaught at the Santiago Bernabeu.
Klopp, though, is promising no miracles ahead of his side's return to the Spanish capital and says he has been in awe of the way that Madrid, who swept aside Schalke 9-2 in the previous round, have evolved into an even more formidable team over the past 12 months.
"I'm not a magician but we have had to get over much adversity this season," the German coach told reporters on Tuesday, referring to his side's many injury problems.
"I have very good players and my duty is to make them better; so far we've done that very well.
"Our players that don't feature in every game are going to grow up in this match. Real Madrid are more flexible now. The speed of their game is amazing.
"Barcelona, Madrid and Bayern are the best. We have to keep on evolving. Last year we were a barrier for Madrid and we are going to try to do that again.
"Playing the second leg at home may be a slight advantage but I fear Madrid trying to settle the tie here. I have seen many of their games and they never finish a match without one scoring opportunity.
"They have incredible quality and we can't ignore that. If we play our game and keep our heads up, we will have chances."
Klopp is not worried about his side's underdog tag, however, as he claims they are used to it in European competition nowadays.
"This Bernabeu is amazing and we are going to need 'cojones'," he added. "Madrid are favourites but they've also had their problems this season, although they're better now with Gareth Bale and with Angel Di Maria showing all their quality.
"We are used to not being favourites and becoming uncomfortable opponents. Nobody should leave us spaces because we can be very dangerous.
"It won't be a catastrophe if we lose. Not many teams can say they have done what we have achieved in the last 10 years.
"Maybe we won't have possession but one-on-one duels could be decisive, although Robert Lewandowski's [suspension-induced] absence is a pity for us.
"We are not ready to play without him but we are going to do our best. Let's see what happens."