Despite a promising second leg showing, Liverpool were unable to overturn last week's 3-1 deficit. The 0-0 draw now means the Reds need a top four finish to guarantee Champions League football for next season.
After the game, Jurgen Klopp spoke to BT Sport about his side's performance.
"The performance was good - we lost the tie in Madrid."
As fans have become accustomed to over the years, Liverpool were quick out of the blocks. Mohamed Salah spurned a great chance to open the scoring after firing a close effort at Thibaut Courtois' legs. Later on in the half, the Belgian was forced into another crucial save, clawing away James Milner's curling effort.
"It was uncomfortable for Madrid - we were aggressive - we had massive chances at the start of the game - you use one of them and it opens it up."
Ultimately, the second half followed the same script: the ball just would not go in for Klopp's side. Despite chances for Roberto Fimino, Diogo Jota and Mohamed Salah, Real Madrid always seemed to get a body in the way.
"Our lack of finishing is a little bit like ourselves this year. We have to take that. We know how often Mo Salah has finished these chances with closed eyes. In this moment, he didn't. Same with Bobby."
Alisson was also brought into action, brilliantly preventing both Vinicius Junior and Karim Benzema from grabbing a decisive goal.
"It got more and more difficult - with the experience of Madrid - they played it down. That is how it is."
"We lost some rhythm in the second half - we needed width. You need to force situations more often. Tonight, it was absolutely okay but we are out anyway."
As aforementioned, Liverpool now need a top four finish to secure qualification to Europe's premium competition.
Although tonight's result is ultimately disappointing, Klopp can take loads of positives from tonight, ahead of their final seven games of the season.
"The Champions League is very important for this club for different reasons. We can now concentrate on the Premier League. That is what we will do. Leeds will be a proper challenge. We have to work our socks off."