Any hopes Manchester United had of salvaging some European silverware from the wreckage of their humiliating Champions League exit earlier in the season were extinguished on a night when Sir Alex Ferguson's side were comprehensively beaten by an Athletic Bilbao team that outclassed and outplayed them for long periods.

Do not be fooled by the scoreline. Wayne Rooney's superb goal came towards the end of a second half that Bilbao had dominated en route to a thoroughly deserved victory that secured them a place in the quarter-finals of the Europa League. United, in truth, never looked like turning around the tie around after the 3-2 defeat at Old Trafford in the first leg and the only surprise was that Bilbao failed to inflict further damage as they carved their opponents open time and again.

Fernando Llorente's sumptuous volley, which was reminiscent of the goal that Robin van Persie scored against Everton in December, gave Bilbao the perfect start before Oscar de Marcos put them 5-2 up on aggregate when he crashed the ball home in the second half following yet another raid on United's left flank, where Patrice Evra endured a torrid evening up against the outstanding Andoni Iraola, who broke forward from right-back to wreak havoc.

Only Bilbao's profligacy spared United more misery at the end of a dismal European season that everyone at Old Trafford will be keen to forget. United lost four of their 10 games in the Champions League and the Europa League and it is worth remembering that this latest setback came against a Bilbao side that are seventh in La Liga, 33 points behind the leaders, Real Madrid. The natural conclusion to draw would be that the Premier League has a lot of catching up to do.

San Mamés was rocking come the final whistle as the home supporters cherished the sight of one of the great clubs in European football being vanquished. Marcelo Bielsa's side are a joy to behold. As well as playing with attacking adventure they possess an indefatigable spirit and work ethic that was epitomised by the sight of Iker Muniain, one of their most creative players, chasing back to rob Rooney of the ball in the left-back spot in the second half.

By that point the Basques were well on their way to victory. Ferguson had said beforehand that Bilbao had a "tremendous advantage" going into this game and it took only 23 minutes for the home side to put themselves in an even better position through a goal of the highest quality. Fernando Amorebieta's raking diagonal pass from inside his own half picked out Llorente who allowed the ball to drop over his shoulder before hitting it on the full, his exquisite volley flashing beyond David de Gea and into the far corner of the net, with Rio Ferdinand completely disorientated.

It was a wonderful piece of skill and provided further evidence of why the Spain international is coveted by the leading clubs in Europe. The only disappointment for Bilbao was that Llorente, who had been struggling all week with a hamstring injury, had to be replaced soon afterwards. The striker could, however, reflect that it was a case of job done as he departed to a standing ovation from the Bilbao fans.

United now needed to score three times, which never seemed likely after a first half when they huffed and puffed with little success. Ashley Young had a shot blocked by Amorebieta after breaking through on the left, Tom Cleverley had claims for a penalty turned down when Markel Susaeta clipped his heels shortly after Llorente's goal and Ryan Giggs saw his far-post header deflected over the bar but that was about as much as we saw from United as an attacking force before the interval.

Little changed after the restart as Bilbao continued to dominate. Iraola came close to scoring a memorable individual goal as he ran on to Susaeta's cutback before skipping past Michael Carrick, dancing around Jonny Evans and beating Ferdinand, but after making all the hard work look easy he steered his left-footed shot from little more than six yards past the post. Another gilt-edged chance went begging moments later when Gaizka Toquero, Llorente's replacement, failed to hit the target with only De Gea to beat.

The inevitable second goal arrived in the 66th minute when Iraola escaped on the right for the umpteenth time and delivered a centre that dropped at the feet of De Marcos, who should have put Bilbao ahead in the 14th minute only to slice horribly wide after Muniain's shot had come back off the upright. This time the midfielder made no mistake. Susaeta and Toquero both came close to adding a third goal before Rooney's 25-yard curling effort finally gave the travelling fans something to cheer.