The Midlands club were 3 out of 3 in the competition before this game, but have been brought back down to earth.
Tyrone Mings' penalty howler gifted the win to Brugge.
Manager Unai Emery knew the game would be tough going into the match on Wednesday.
“We played a very good first half and created chances to score but we didn’t score,” Emery reflected on the 1-0 loss.
“We conceded a couple of chances but we were more or less controlling the match and we knew our way.
“In the second half, the mistake changed everything because one team like them, playing at home, they’re defensively strong, very focused and playing 100% in their idea to stop us and play in transition. They were better than us.
“The key was the first half and then the mistake we made.”