Pain in Spain for Bhoys
Sonny Anderson and Roger Garcia capitalised on some sloppy play in the Hoops backline by Bobo Balde and Joos Valgaeren in each half to guide Villarreal into the last four.
Celtic's chances were hit before kick-off when Chris Sutton failed to recover from a groin injury. The Hoops were already weakened by the suspension of Alan Thompson.
Celtic manager Martin O'Neill blamed defeat on individual mistakes and the absence of key players.
O'Neill admitted his side missed Chris Sutton's presence but has no regrets about playing him in the Tennent's Scottish Cup semi-final win over Livingston, when he scored twice but suffered a recurrence on a long-standing injury.
O'Neill was critical of Bobo Balde and Joos Valgaeren after they gifted Villarreal their goals.
"I thought that the first goal was avoidable," O'Neill added. "It certainly put us on the back foot for 10 minutes.
Celtic made the worst possible start as they fell behind after just six minutes.
Juliano Belletti hung the ball in the air from the right and Anderson reacted to hesitancy from Balde to head the ball over an exposed David Marshall from just inside the box.
Balde was having a shocker and was lucky to escape another moment of weakness in the 13th minute.
Mari was able to take the ball down and burst into the box, with Balde failing to put in a decent challenge, but his stretching leg could only fire over the crossbar from 14 yards.
With Larsson alone in attack they struggled to cause Villarreal's defence any bother and their wall comfortably coped with Stanislav Varga's shot after 23 minutes.
Celtic came back into it after that but Miller was unable to keep a hopeful right-foot swipe down after Henrik Larsson had picked him out in the box.
Celtic had good claims for a penalty on the half-hour as McNamara seemed to get tripped in the box by Rodolfo Arruabarrena in the box.
There were encouraging signs for Celtic as Anderson deflected Stilian Petrov's free-kick wide before squandering a glorious chance to go level in the 32nd minute.
McNamara swung an inviting cross into the box and Stephen Pearson came in and jumped high over the Villarreal defence but headed over from just eight yards.
Valgaeren could have gone some way to saving Balde's blushes when he was put through by Petrov. The Belgian was still faced with a difficult angle but he got a shot away which was well blocked by goalkeeper Jose Reina.
Celtic stepped up the tempo after the break but the Villarreal defence were stronger than the visiting backline.
They did look vulnerable though in the 55th minute when Larsson got on the end of Didier Agathe's cross to head wide with Valgaeren just unable to steer the ball home.
Mari could have put the game out of Celtic's reach in the 58th minute but he wildly slashed his effort over.
Balde made amends for his early low point, moments later, when a crucial last-ditch tackle in the box blocked Anderson's strike.
Miller could have equalised in the 62nd minute when Lennon's free-kick hit Varga and landed at his feet but he blazed his left-foot shot high and wide. Celtic's mission became impossible in the 68th minute when Villarreal increased their advantage.
Anderson was the provider as he crossed from the left and Garcia showed more desire than Valgaeren and blasted the ball past Marshall.
O'Neill made a double substitution in the 70th minute with Jamie Smith and Ross Wallace replacing Miller and Pearson. Sebastian Battaglia became the next man booked for a foul on Petrov before Larsson fired the free-kick high over which summed up Celtic's gloomy night.
: Reina, Arruabarrena, Coloccini, Belletti, Ballesteros, Josico, Roger, Battaglia, Riquelme, Jose Mari (Javi Venta 85), Anderson.
: Marshall, McNamara, Valgaeren, Balde, Varga, Agathe, Lennon, Miller (Smith 71), Petrov, Larsson, Pearson (Wallace 71).
: Massimo De Santis (Italy).
Valencia beat Bordeaux 2-1 to clinch a 4-2 aggregate win and set-up a semi-final showdown against countrymen Villarreal.
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