Having lost 3-2 at Old Trafford last week, the Reds' second-leg task was always going to be tough. The job was made all the more difficult when Fernando Llorente, such a handful in the first game, smashed home a stunning volley on 23 minutes.
The Basque side, seventh in La Liga, then produced a masterclass in possession and pressing and deservedly doubled their lead on the night when Oscar de Marcos beat David De Gea with a deflected shot in the 66th minute.
Wayne Rooney's wonder goal gave United a glimmer of hope for the final ten minutes, but in truth it was too little too late for the Reds. Sir Alex's men, outplayed over two legs by a side packed with talent and potential, were out of Europe and could have no complaints.
The manager had made three changes to the team that lost the first leg at Old Trafford. Rio Ferdinand replaced Chris Smalling in defence, while Michael Carrick and Tom Cleverley both came into the centre of midfield to play alongside Ryan Giggs, who was given licence to push forward and support Wayne Rooney in attack. Ashley Young and Ji-sung Park occupied the wide positions.
Marcelo Bielsa, meanwhile, made just one change to his Athletic side that left Old Trafford victorious last week: defender Fernando Amorebieta, suspended for the first leg, took the place of Mikel San Jose in the heart of defence.