Birmingham keeper Colin Doyle made a complete hash of a Jonathan Spector back-pass which gifted the Slovenian side a 1-0 lead. But the Championship outfit fought back to win 2-1 with strikes from Chris Burke before Wade Elliott.
"Overall I thought it was a good game," said Blues chief Chris Hughton.
"From my point of view I was very frustrated with the first goal we conceded and one of the reasons we're happy we won is because we wouldn't have liked to have lost to a goal like that.
"We showed great character and team spirit and in the end I thought we were worthy winners.
"You do reflect on goals like that and it's always good to clear things up after mistakes. In defence of Colin, it was a very difficult ball for him to deal with. It was then important we didn't concede again and we managed that and then went on to get a grip on the game."
Hughton added: "I would think Colin and Jonathan might offer to buy Chris and Wade a drink now!"
"These things are part and parcel of the game. Their goal was very much a mistake. Anybody can make them and it just makes us more thankful to get the result.
"Someone made a mistake today and someone else might make the next one. That's football."
While his side lie 19th in the Championship, Hughton is still determined to make the most of his side's European adventure.
"Of course we want to do well in this competition," he said.
"The most important thing for us is competing and we know Brugge and Braga are very experienced and have so much quality."