Arsene Wenger accused Braga of using "every trick in the book" as Arsenal failed to book their place in the Champions League last 16.
The Gunners went down 2-0 in Portugal to leave them still not guaranteed a place in the knockout stage - and they are also set to miss captain Cesc Fabregas for a couple of weeks with a hamstring problem.
The Gunners - beaten by rivals Tottenham on Saturday - had been top of Group H and thrashed the Portuguese side 6-0 in their opening fixture.
However, a much-changed side never hit top gear against stubborn opposition.
Indeed, Arsenal were denied a cast-iron penalty by Hungarian referee Viktor Kassai when substitute Carlos Vela was fouled by Alberto Rodriguez before Braga scored two late breakaway goals from Brazil striker Matheus to leave Wenger's men needing to beat Partizan Belgrade at home in a fortnight to make sure of a place in the knockout stages.
"We played against a team who refused to play and tried to catch us on the counter attack. They used every single trick in the book to slow the game down," Wenger lamented.
"We were not sharp enough to create clear-cut chances.
"Saturday's result had no knock-on effect, because I had seven players who did not play, and I had to rest some players.
"I think we had enough on the pitch to make a goal, but football is like that when the other team focuses not to play.
"Everybody is free to play the way they like, and they won.
"We could play 10 matches like that and win eight or nine times, but tonight was the one we didn't."
Wenger was in no doubt his side should have been given a spot-kick and hit out at the use of two extra officials by UEFA.
"It is difficult to understand how we did not get a penalty," he said.
"The five referees is not an answer to the problem.
"We were caught when Eboue was just down on a bad tackle which went unpunished.
"The turning point was the penalty - I still cannot understand how Carlos Vela got a yellow card. It remains a complete mystery.
"The referee had some surprising decisions tonight.
"It is hard to swallow, but now we have to win our last game.
"The most important thing for us now is to qualify.
"It is good that Shakhtar play against Braga, but they are the super favourites to win the group."
On the officials, Wenger continued: "We are going through a period where we have bad luck, we had Eboue kicked off the park without any punishment and we also had the penalty turned down.
"What was the fifth official doing? We have another proof that it is absolutely useless, this system.
"Then when we were 10 against 11, we made a mistake at the back, there was a minimum of communication and that's where we were punished."
Wenger hopes Arsenal's injuries will not prove too bad.
"Eboue will be out for a while and we will have to asses Fabregas tomorrow. It could be two to three weeks," he said.
"It is very disappointing because I had a hesitation to play him before the match started.
"I took the gamble and it backfired on us."
Braga coach Domingos Paciencia refused to be drawn on Wenger's blast.
"I don't want to comment, because it is just the personal opinion of the Arsenal manager," he said.
On the penalty, Paciencia said: "I have seen it on TV, but before there was an offside, so first should be offside, then no penalty would be allowed for Arsenal."
Braga, the Champions League debutants, are now level on points with Arsenal and could yet pull off a shock to reach the last 16.
Paciencia said: "It is very difficult, but we have to believe we can do it until the very end.
"It will be a tough game against Shakhtar, but we still feel it is possible."
