The Serbian saw his 11th-minute spot-kick saved by goalkeeper Quim and the Portuguese hosts went on to claim victory thanks to a touch of City misfortune as Hugo Viana's 50th-minute strike took a huge deflection off Curtis Davies.
The result saw Braga qualify for the last 32 from a tight Group H based on their head-to-head record and a 3-1 victory at St Andrew's on matchday one, while Club Brugge's dramatic fight back to claim a 4-3 victory over bottom club Maribor also sent them three points clear of City.
It left Blues needing to defeat Maribor in the final round of fixtures and hope Brugge and Braga do not play out a draw which would see the Belgium side through.
The visitors, attacking the iconic end containing the backdrop of a rock wall of the quarry within which the stadium stands, made a positive start in front of a sparse crowd.
Wade Elliott and Chris Burke were enjoying particular success down the right channel and it was from that area that the former won a penalty for Blues when he was brought down by Ewerton on the edge of the box.
However, Zigic saw the golden opportunity slip from his grasp as Quim dived to his left to produce a great parried save.
The Braga stopper was again called into action to keep out David Murphy's free-kick and skipper Steven Caldwell's header.
Braga steadied the ship after the early pressure and kept possession well, although only Mossoro went relatively close with a curled effort.
Despite Braga's neat approach play, City goalkeeper Boaz Myhill was still to make a save of note.
Helder Barbosa passed up a great chance to test the Welshman as half-time approached but he completely fluffed his attempted shot from Alan's low pass.
Keith Fahey could have made the Portuguese side pay at the other end but saw his low drive well swallowed up by Quim on the stroke of half-time.
Yet just minutes after half-time Hughton's side saw all their good work unravelled thanks to a chunk of misfortune.
Viana, formerly of Newcastle, received the ball 30 yards out and his left-footed effort took a huge deflection off the unfortunate Davies and wrong-footed Myhill.
Barbosa was again guilty of missing a great opportunity when he fluffed his lines for a second time, on this occasion when trying to convert Mossoro's pass.
Hughton turned to substitute Marlon King in his attempt to get Blues back into the game but it was Braga who were threatening a second goal, with Barbosa seeing his teasing ball across the face of goal fail to find a red shirt.
King and Burke got in each other's way when either man could have scored the equaliser while 10 minutes from time Lima was clean through on goal but denied by Myhill, with Paulo Cesar somehow spooning the rebound over the bar.
To compound Blues' misery, Brugge completed their comeback to claim a dramatic victory and take qualification out of the hands of the midlands club.