"It's disappointing but we gave it our all in every moment," Lopez told UEFA.com. "We were missing that small bit of luck.
"The fans are the standout aspect for me tonight as ever since we arrived at the ground in the team bus they created a spectacular atmosphere. They trusted in us and brought us a lot in the game.
"We felt that taking an advantage into half time was going to be the key but even so, we had chances in the second half to score the three goals we needed. We believed in ourselves but at the end of the day it didn't happen. We are leaving in good conscience. We need to wish Dortmund good luck and move on."
Madrid last won the Champions League in 2002.