The defender saw the positives in European elimination at the hands of Carlo Ancelotti's side and admitted his thoughts are "conflicted" after a top displayMats Hummels described Borussia Dortmund's exit as an "awesome evening" despite being gutted to have been eliminated from the Champions League by Real Madrid on Tuesday.
The Schwarzgelben put up quite the fight, beating the Blancos 2-0 at Signal Iduna Park having gone into the tie 3-0 down, but their valiant performance was not enough to see them into the last four for a second consecutive season.
Instead, the team they knocked out at the semi-finals a year ago got revenge in Dortmund, but Hummels was proud of the performance and says it shows how good the team can be when faced with a great challenge.
"I am conflicted," the centre-back is quoted as telling reporters after the match. "We showed an evening that people won't forget quickly.
"We had several great chances in the second half. We could have produced one of the biggest sensations in football - now it was just an awesome evening.
"The team prove every year, again, what we have to offer. The fans were so noisy we couldn't hear each other."
Bayern Munich have already wrapped up the Bundesliga title race, but Dortmund can still win silverware if they make it through the semi-final stage of the DFB-Pokal.