Jurgen Klopp's side beat Real Madrid 2-0 in the second leg of their quarter-final tie, but were knocked out of the competition due to a 3-2 aggregate result.
However, Hummels was keen to remain positive as he praised the support of the home fans for their part in a thrilling end to the meeting with the Spanish club.
"I am conflicted," the defender told reporters. "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."
Dortmund return to action in the Bundesliga on Saturday against Bayern Munich.