Sir Alex Ferguson's men are outplayed by their hosts and never get close to qualifying for the next round as they are thoroughly beaten by the Marco Bielsa's side
The hosts were on the front foot for almost the entire match, as United were put to the sword thanks to some high intensity play with plenty of technique on display.
Sir Alex Ferguson opted to go with Wayne Rooney as the lone striker, backed up by Ryan Giggs in an attacking role.
Ashley Young was deployed on the left wing, with Park Ji-Sung on the right and a central pairing of Tom Cleverley and Michael Carrick.
Athletic lined up with a similar team to those who impressed at Old Trafford, with Iker Muniain and Llorente the main attacking threats for the hosts.
And United attacked straight from the off, as Park found Rooney down the left, but the striker got his chip all wrong as it went across the face of goal.
It looked certain to be an end-to-end game, with the home side swarming around the ball when United were in possession, and attacking with vigour when on the ball.
Young was the next player to go close, put through by Cleverley but seeing his shot blocked before Marcelo Bielsa's men almost put the tie beyond United.
Llorente played a neat reverse pass through to Muniain, open on the edge of the area, and when his low drive cannoned back off the post and back to De Marcos, it looked grave for the English champions.
But De Marcos conspired to heave an effort over the bar with David de Gea out of position after the initial shot. It was a huge let off for United.
But it wasn't long before the visitors were behind, to a fantastic finish by Llorente. A simple long ball over the top from Amorebietta exposed Rio Ferdinand, and the Spanish striker volleyed it across the face of goal and into the far corner, giving De Gea no chance.
It meant that United went 4-2 down on aggregate and would need at least three goals to advance to the next stage.
A fabulous cross from Young to the back post five minutes later found an un-marked Ryan Giggs, but his header was brilliantly blocked by one of the Athletic defenders to deflect it over the bar.
The next flash point came when Cleverley controlled a ball on the edge of the box and took a knock on the led from a Bilbao defender, but nothing was given as the midfielder went down fairly easily.
The half ended with both sides already nursing injuries, as goal scorer Llorente was substituted five minutes before the end, and Rafael fell awkwardly on a soft patch of grass, but seemed to recover before the break.
Going into the second half Ferguson's side still needed three goals, and didn't look like getting anywhere near that target as Athletic bombarded them.
The hosts were inches away from an astounding goal as Andoni Iraola threw in a couple of stepovers on the edge of the box, rolling the ball past first Carrick then Ferdinand, but placing his shot just wide of the post, with the home crowd about to take the roof off the stadium.
Time and again United were forced to kick the ball long under immense pressure from the hosts, and they just could not get their own game going with Rooney looking out of sorts after little time at all on the ball.
Ferguson perhaps gave a telling sign of how he thought the game was progressing just after the hour mark when he withdrew Ferdinand and Carrick for Chris Smalling and the promising but inexperienced midfielder Paul Pogba.
And two minutes later United's European misery was all but sealed. A cross in towards Toquero was well blocked by Smalling, but the rebound fell to De Marcos 10 yards out, and his shot was deflected past De Gea by the outstretched foot of Jonny Evans.
Even as the match progressed and Danny Welbeck was introduced, United continued to struggle and failed to create any chances.
It was, in fact, Athletic who were coming closer and closer to adding a goal, as Iraola's great cross was inexpleicably headed over from six yards by Toquero.
It was another poor European night for United, and the final one of the season for them. Rooney went down with what looked like a nasty tackle on his ankle, but recovered to carry on.
Rooney recovered so well, in fact, that he was able to curl a beautfiul effort into the top corner to bring a goal back for the visitors, and it was even applauded by the home fans.
United were starting to look like they had a way back into the game, with Rooney the chief player creating. But De Marcos almost snatched another with a little under five minutes remaining.
Welbeck came close from long range, forcing the first save of the night from Iraizoz, but the keeper did well to push it around the post.
Ultimately though, United were nowhere near their peak, and suffered as they were outplayed by the hosts in every department, and deservedly knocked out of Europe for a second time this season.