Celtic exited the Europa League at the last-32 stage with a 1-0 defeat in Valencia but pride was evident on a night of some frustration in the Mestalla.
The Spanish side impressed in their 2-0 first-leg win in Glasgow last week but they were outplayed by a bullish Hoops side until the 37th minute when right-back Jeremy Toljan was sent off by referee Deniz Aytekin for picking up a second yellow card.
The 10 men kept going valiantly in the second half but were undone in the 70th minute by a goal from substitute Kevin Gameiro which gave the home side a 3-0 aggregate win.
The Scottish champions were knocked out at the same stage of the tournament last season by Zenit St Petersburg.
Brendan Rodgers' team will lick their European wounds again and concentrate on the domestic scene where they are eight points clear at the top of the Ladbrokes Premiership and continuing their quest for an unprecedented domestic treble-treble
It was always going to be a tough night for Celtic.
They had never won in Spain but with defender Jozo Simunovic reinstated into a back three at the expense of winger Scott Sinclair, with on-loan striker Oliver Burke in for Odsonne Edouard, they made more than a good fist of the first half.
Jonny Hayes' run down the left flank in the fourth minute - his drive was well held by Valencia goalkeeper Neto - offered some early hope.
So too, did a ninth minute Ryan Christie corner which ended with Kristoffer Ajer's drive blocked by midfielder Daniel Wass, his second effort flying over.
The hosts, ninth in LaLiga, looked slovenly if not complacent.
Former Arsenal player Francis Coquelin replaced injured Ezequiel Garay before referee Aytekin booked Hoops skipper Scott Brown and Toljan for fouls on Goncalo Guedes.
Burke's pace and power were causing Valencia problems.
Another run down the left ended with a Celtic corner, this time Simunovic's header going straight to Neto, who watched a Hayes drive in the 35th minute miss his post by a yard.
Two minutes later, however, the dynamic changed when Toljan, on loan from Borussia Dortmund, was sent packing for impeding Guedes 35 yards from goal, the free-kick coming to nothing.
Ajer moved to right-back in a reshuffle and in the 42nd minute Celtic keeper Scott Bain had his first real save to make from skipper Daniel Parejo's deflected drive from the edge of the box and again moments later from a Santi Mina shot as the Spanish side finished the half on top.
Valencia attacked in waves at the start of the second period.
Simunovic hooked an angled drive from Mina away from the line, before Bain plucked a Wass volley out the air.
Then Ajer got his head to Christie's whipped-in free-kick only to miss the target from close range.
Edouard replaced James Forrest in the 63rd minute but it was Valencia's replacement Gameiro who made an impact three minutes after he came on for Ruben Sobrino, bundling in Wass' header from six yards following a deep Parejo cross.
That was it effectively over for rapidly tiring Celtic who were on the ropes in the final minutes, Bain making a fine save from substitute Kangin Lee.