The Spanish giants lost 1-0 at home at the Bernabeu, after a late goal by Yossi Benayoun.
But Pepe is confident Real can turn things around in the second leg at Anfield in two weeks’ time.
He said: “Logically, we are disappointed with this result as we let the match slip away because of a silly error from a set-piece.
“But throughout the entire game, the big mistake that we all made was that we couldn’t break down Liverpool’s defensive system.
“They had two lines of four in front of their goalkeeper at all times and that made it impossible for us.
“But we will go to Anfield with the mentality that we can overturn this tie.
“We are going there with the kind of winning spirit that has always characterised Real Madrid.
“It’s very unpleasant to take a 1-0 deficit there but we are going to do everything to make it up to our fans.
“It is necessary to have faith that we can achieve it.”