They felt the 3-0 score line flattered the German club, runners-up in last season's final, and that they let slip opportunities in their first game of the group phase of the new-look competition.
Brugge were arguably the better side for 76 minutes at the Jan Breydelstadion but then conceded twice to Dortmund substitute Jamie Gittens and gave away a late penalty that Serhou Guirassy converted.
"We played good football and created chances and also gave little away for an hour," goalkeeper Simon Mignolet said.
"But you have to seize your moments in such matches. If we had taken the lead, we would have had even more chances on the counter. But that did not happen.
"Dortmund also has a very extensive squad and it was a gruelling match. When they can bring on fresh guys – top talents – then you have a hard time."
"This could definitely have been a point," added captain Hans Vanaken.
"For 75 minutes we played very well and even created the most chances. It’s a shame we couldn’t score."
Coach Nicky Hayen said he had mixed feelings.
"It tastes very sour as far as the final result is concerned, at least," he told reporters.
"But I do have a positive feeling about the first 75 minutes. We made it difficult for Dortmund, and I am happy with the way we showed ourselves.
"If we do that again next time, we can win points everywhere. But we have to learn to take our chances when they present themselves and we didn't do that."
Hayen said before the match the Belgian champions were aiming for a top 24 finish in the new format, which would see them into the knockout round plays off in February.
Their next Champions League clash is away at Austria’s Sturm Graz on October 2
