Twice the Celtic offside trap was broken with ease either side of half-time as Ruben Sobrino’s pass was tapped home by Denis Cheryshev before the Russian turned provider for Sobrino to net on his Valencia debut after a January move from Alaves.
Brendan Rodgers’s men now have a mountain to climb when the sides meet for the second leg of the last 32 tie in Spain on February 21 given the gulf in class on show between the Scottish champions and the side that finish fourth in La Liga last season.
Only Salzburg in the group stages of the Europa League had emerged victorious from a visit to Celtic Park previously this campaign and buoyed by a run of seven straight wins since the winter break in Scotland, the home side started positively.
Callum McGregor forced Valencia goalkeeper Neto to scramble low to his left to turn the ball to safety and James Forrest saw speculative claims for a penalty waived away.
However, Valencia quickly took control with captain Dani Parejo pulling the strings in midfield and only a super save from Scott Bain denied Daniel Wass from opening the scoring with a powerful header.
Celtic often created their own problems by gifting away possession inside their own half and were eventually punished three minutes before the break when Parejo picked out Sobrino’s well-timed run despite the home side’s pleas for an offside flag and he unselfishly squared for Cheryshev to roll into an empty net.
The same two players combined four minutes into the second half as Cheryshev’s teasing cross split Bain and the Celtic defenders for Sobrino to volley home.
The introduction of Odsonne Edouard and PSG loanee Timothy Weah lifted Celtic on the hour mark, but Weah blasted over the hosts’ best chance to get a foothold in the tie.