Celtic's hopes of a second successive UEFA Cup final appearance foundered in the El Madrigal Stadium.
A goal in each half from Sonny Anderson and Roger put Villarreal into the semi-finals as Celtic's European run ran out of steam.
The Spanish side kept their record of never having lost a goal at home in the competition as Celtic failed to give goalkeeper Jose Reina a direct shot to deal with.
Celtic were dealt a blow two hours before kick-off when Chris Sutton failed a fitness test on his groin injury and was ruled out.
With Alan Thompson suspended, it stretched Celtic's resources and Manchester United-bound Liam Miller was given a starting place.
Celtic were stunned after just six minutes when Villarreal took the lead when Anderson crept between Bobo Balde and Stanislav Varga to head a Juliano Belletti cross over David Marshall.
Jose Mari had another chance seven minutes later when he eluded Balde to send a right-foot shot narrowly wide.
A mistake by Neil Lennon on the edge of his own penalty area presented Juan Riquelme with a shooting chance, but he pulled his shot a couple of yards wide.
Celtic gave away possession cheaply early on and had little to offer up front as Henrik Larsson was left isolated up front.
Celtic finally mustered an attack of some substance after 28 minutes when Larsson picked out Miller in the area with a neat cutback, but he sliced his effort well wide.
Jackie McNamara then felt he should have had a penalty when he was barged by Rodolfo Arruabarrena as Celtic showed renewed vigour.
Stephen Pearson was only a foot too high with a header as Villarreal suddenly looked vulnerable.
There was a major let-off for Celtic two minutes from the break when Belletti picked out Anderson again in front of goal but he took his eye off the ball and nudged his header well away from goal.
Celtic lived dangerously again in the 59th minute when Anderson sent Roger clear but he swiped his shot yards wide of goal.
A minute later, it took a last-ditch tackle from Balde to block an Anderson shot when the Brazilian looked set to score.
The killer second goal came in the 68th minute when Roger lashed a left-foot volley past Marshall from an Anderson cross with Joos Valgaeren guilty of hesitation.