Jorge Helder Barbosa's double sealed victory for Braga as Birmingham started life in the Europa League.
Braga opened the scoring in the sixth minute when Nuno Gomes crossed for Barbosa to volley in.
It was 2-0 after 58 minutes when Gomes laid the ball back for Lima, who powerfully finished from 10 yards.
Chris Burke's cross to the back post was tapped in by Marlon King to make it 2-1 on 72 minutes, but Carlao teed up Barbosa for the clincher.
It was a performance full of effort by Birmingham with Nathan Redmond looking excellent at times, delivering some teasing crosses, and Burke also looking dangerous when he came on.
But Braga, last year's finalists, were always a threat going forward and deserved their win. Birmingham's best spell came when they cut the deficit to 2-1 then pressed for an equaliser, but the Portuguese team were capable of counter-attacking fluently.
Birmingham had suffered early on as Braga started well. Goalkeeper Boaz Myhill could have done better in his attempt to stop Barbosa's opening strike, but he could only palm the volley on to the crossbar and the ball ended up in the back of the net.
Myhill responded well to that setback and Chris Hughton's side improved as the first half went on with Redmond having an effort saved and Adam Rooney heading over.
Against the run of play, Birmingham fell further behind. Gomes had knocked the ball back on the edge of the six-yard box and Lima smashed the ball in from 10 yards as the ball went in off the bar.
Burke brought his team back into the game with a lovely pass that was met by King, who timed his run to perfection and scored a deserved goal after a hard-working display.
Hughton's team pushed hard for the equaliser with Redmond producing a 30-yard effort that was pushed away by Quim, but they were a beaten side when Braga broke and Carlao set up Barbosa to tuck in his second from eight yards.
Birmingham boss Chris Hughton: "I've no arguments with the result.
"What we saw in Braga was a team who once they got into the forward areas and close to goal, they were more clinical and showed better quality than we did.
"At 2-1 we were the team in the ascendancy, and if anybody was going to get the next goal, then it was possibly going to be us.
"But when you are playing against a side of the quality of Braga that have the experience they do, there is always the possibility of getting caught on the counter-attack, and that is what happened."
Birmingham: Myhill, Ridgewell, Ibanez, Carr, Murphy, Spector, N'Daw (Burke 60), Elliott, Redmond, Rooney (Wood 60), King. Subs Not Used: Doyle, Caldwell, Beausejour, Davies, Asante.
Goals: King 71.
Braga: Quim, Ewerton, Paulo Vinicius, Echiejile, Baiano, Alan, Djamal, Hugo Viana, Helder Barbosa (Paulo Cesar 89), Lima (Carlao 82), Nuno Gomes (Leandro Salino 73). Subs Not Used: Berni, Mossoro, Merida, Imorou.
Goals: Helder Barbosa 6,Lima 59,Helder Barbosa 88.
Ref: Deniz Aytekin (Germany).