The Portuguese club managed to hold onto their 1-0 lead from the first leg, played at Estadio AXA last Thursday, to move into the final eight of the competition for the first time ever.
After just two wins in their last nine matches away from home in Europe, Braga did what they needed to do against their more-fancied opponents as Kenny Dalglish and his Reds are left to lick their wounds in what is beginning to become a forgettable season on the Merseyside.
Venue: Anfield, LiverpoolCrowd: 37,494 Referee: Gianluca Rocchi Yellow cards:LIV - Andy Carroll 52', Martin Skrtel 70', Raul Meireles 83' BRA - Paulao 52', Vandinho 73'
Liverpool started brightly when Andy Carroll headed a clear path for Joe Cole but his shot was well-saved by Artur Moraes in the 8th minute before Carroll had a chance with the follow-up.
There were encouraging signs for Kenny Dalglish as his Reds were moving the ball around well but it was Braga's Lima who produced the next shot on goal in the 15th minute with a long range strike which was safely held by Pepe Reina.
Carroll's height was again causing a few issues for the Braga defence, as it did in the second half last week, as the Portuguese outfit's defenders were using heavy-handed tactics to deal with the home side's forwards.
The frustration started to mount on the Liverpool players and fans as time progressed with the Braga defence holding strong but they were soon stretched when Dalglish brought on David Ngog and the Frenchman almost had an immediate impact with a shot on goal but Braga keeper Artur was up to the task.
It wasn't looking like Liverpool's night, especially when Dirk Kuyt headed on target but it was kept out by a Braga defender before Raul Meireles came in for the follow-up by Artur was there to deny him.
The frustration grew in the dying minutes as Domingos Paciencia's men held firm and managed to put themselves into the next round of the competition.
Liverpool Pepe Reina (gk) - Jamie Carragher, Glen Johnson, Martin Skrtel, Danny Wilson - Joe Cole (Ngog 75'), Raul Meireles, Lucas, Maxi Rodriguez (Spearing 75') - Dirk Kuyt, Andy Carroll
Subs - Peter Gulacsi (gk), Jay Spearing (75'), David Ngog (75'), Sotirios Kyrgiakos, John Flanagan, Christian Poulsen, Dani Pacheco
Subs - Cristiano Figueiredo (gk), Kaka (74'), Albert Ze Meyong (84'), Mossoro (89'), Coelho Dani, Peterson Joseph, Helder Barbosa