The shot stopper feels the Spanish champions could have made it to the final at Wembley had they had been more fortunate on Tuesday
Jose Mourinho's men found themselves on the verge of elimination after losing last week's first leg 4-1 at the Signal Iduna Park but they came close to reaching the final with a 2-0 win in the return.
"It's disappointing but we gave it our all in every moment. We were missing that small bit of luck," the goalkeeper was quoted as saying on the official Uefa website.
"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 resume domestic action on Saturday when they host Valladolid.