Match ends, Valencia 1, Celtic 0.
Celtic's Europa League campaign ended at the last-32 stage for the second successive season as they were knocked out by Valencia.
Their task in the second leg always looked formidable, given they had never overturned a two-goal deficit away from home, nor had they won in Spain.
A creditable first-half performance was marred by Jeremy Toljan's dismissal for twice pulling back Goncalo Guedes.
And Celtic finally conceded when Kevin Gameiro forced home from close range.
While the Glasgow side were passive last week at Celtic Park, they were far more aggressive at the Mestalla.
Jonny Hayes shot over for the visitors, while Kristoffer Ajer also went close with the game still goalless.
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Hopes faded with Toljan exit
It would be stretching it to suggest Toljan's red card was a pivotal point in the tie, with Valencia well in command following their 2-0 win at Celtic Park last week.
But Celtic had at least given them food for thought, with a 3-4-3 formation offering a much more solid look and their use of the ball far improved.
Ajer had a goalbound shot blocked and Jozo Simunovic's header was comfortably saved as Celtic searched for the opening goal that would bring the tie alive. Ajer would also bullet a glorious header over the bar later in the match with the game still goalless.
But their faint hopes of recovery vanished as Toljan was punished twice in quick succession for dragging Guedes down after allowing him to get goal-side.
That prompted Valencia to waken from their slumbers and Scott Bain saved brilliantly twice before half-time - keeping out a Daniel Parejo shot that had deflected off Ryan Christie, then tipping away Santi Mina's net-bound effort.
He and the rest of the Celtic defence stood firm for 25 minutes of the second half in the face of increasing pressure before finally buckling.
Guedes' fabulous diagonal ball from the left was headed into the six-yard box by the advanced full-back Daniel Wass, and Gameiro - only just on the field - bundled it through the legs of Bain with his knee.
The Celtic keeper was called upon twice more before the end but that was as damaging as it got for Celtic, though the principal wounds were inflicted in Glasgow a week ago.
Tangible progress in Europe no closer - analysis
Just as overcoming Zenit St Petersburg last season proved a bridge too far for Brendan Rodgers' side, the team sitting ninth in La Liga were also too good for the Scottish champions.
While they continue to sweep away all before them domestically - with a treble treble still a possibility - tangible progress on the European front looks no closer.
Certainly, there is a financial disparity between Zenit, Valencia and Celtic, but the same was true when both Glasgow clubs reached the final of the Uefa Cup.
Both Martin O'Neill and Walter Smith found ways to overcome teams like Liverpool and Werder Bremen, outdoing them tactically, maximising the undoubted talent in their squads.
Celtic, in three seasons under Rodgers, have yet to claim a really noteworthy scalp.
- Celtic have not won a knockout away game in Europe since beating Boavista 1-0 in April 2003, losing eight of their nine games since. They have also failed to score on all nine occasions
- They have never won away from home against a Spanish side (P18 W0 D3 L15), losing to Valencia three times.
- Celtic have failed to score in consecutive European games for the first time since September 2016.
- Toljan was the second Celtic player to receive a red card in this season's Europa League after James Forrest's sending-off against Red Bull Salzburg in October
- 13Murara Neto
- 18WassSubstituted forLeeat 76'minutes
- 24GaraySubstituted forCoquelinat 23'minutes
- 12DiakhabyBooked at 53mins
- 15Latorre Grueso
- 7Gonçalo Guedes
- 22Mina Lorenzo
- 23SobrinoSubstituted forGameiroat 68'minutes
- 2ToljanBooked at 37mins
- 15HayesBooked at 58mins
- 49ForrestSubstituted forEdouardat 63'minutes
- 8BrownBooked at 24mins
- 25BurkeSubstituted forJohnstonat 73'minutes
- Deniz Aytekin
- Shots on Target
Second Half ends, Valencia 1, Celtic 0.
Attempt saved. Lee Kang-In (Valencia) header from very close range is saved in the centre of the goal. Assisted by Kevin Gameiro.
Attempt missed. Kevin Gameiro (Valencia) right footed shot from the centre of the box misses to the right. Assisted by Ferrán Torres.
Kevin Gameiro (Valencia) wins a free kick in the attacking half.
Foul by Jozo Simunovic (Celtic).
Attempt blocked. Michael Johnston (Celtic) right footed shot from outside the box is blocked. Assisted by Callum McGregor.
Attempt saved. Santi Mina (Valencia) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Ferrán Torres with a cross.
Attempt missed. Santi Mina (Valencia) right footed shot from the left side of the box is close, but misses the top right corner. Assisted by Gonçalo Guedes.
Attempt blocked. Lee Kang-In (Valencia) left footed shot from the right side of the box is blocked. Assisted by Ferrán Torres.
Foul by Ferrán Torres (Valencia).
Odsonne Edouard (Celtic) wins a free kick on the left wing.
Attempt blocked. Scott Brown (Celtic) right footed shot from outside the box is blocked. Assisted by Odsonne Edouard.
Attempt blocked. Gonçalo Guedes (Valencia) right footed shot from outside the box is blocked. Assisted by Toni Lato.
Attempt blocked. Scott Brown (Celtic) right footed shot from outside the box is blocked.
Foul by Francis Coquelin (Valencia).
Jonny Hayes (Celtic) wins a free kick in the defensive half.
Substitution, Valencia. Lee Kang-In replaces Daniel Wass.
Corner, Valencia. Conceded by Dedryck Boyata.
Attempt blocked. Santi Mina (Valencia) right footed shot from outside the box is blocked. Assisted by Kevin Gameiro.