The Portugal international has not given up hope of making it to the final yet as and believes los Blancos can set the record straight at home
Four goals from Robert Lewandowski helped BVB to an impressive home victory, with Cristiano Ronaldo scoring Madrid's only goal of the game, but Pepe is confident that Jose Mourinho's men have what it takes to turn things around in the return.
"Obviously we're not happy with the result tonight, but if there's one team who can turn this tie around on home turf, it's us, Real Madrid," Pepe told uefa.com.
"We need to score three goals in the return leg and that's not impossible for us. We've done it many times before, especially at home.
"We didn't start either half well on Wednesday and kept making the same old mistakes. If we can sort that out and fight for every minute of the second leg as if it were our last, we can still reach the final."
Madrid lock horns with city-rivals Atletico at the weekend before turning their attention to Tuesday's return against BVB at the Santiago Bernabeu.