Celtic were easily beaten at Parkhead by the La Liga outfit.
The 18-year-old was used as a substitute by Brendan Rodgers again, coming on with 30 minutes remaining and the Paris Saint-Germain loanee failed to have an impact - as did much of the Celtic squad.
Denis Cheryshev, one of Russia's stars at last summer's World Cup, opened the scoring before putting an excellent cross into the path of Ruben Sobrino who fired a second past Scott Bain.
Celtic looked flat and were unable to even fire a shot on target in the second half. Weah himself had a chance, but blazed a bouncing ball over the bar from 18 yards out. He posted on Instagram after the match.
Celtic failed at the last 32 stage of the Europa League last season, losing to Russian side Zenit St. Petersburg. They will have to produce a mammoth performance to overcome the Spaniards in their back yard next week.
Since joining Celtic on loan, Weah has scored three goals in eight appearances for the Hoops, but he could do nothing to prevent Valencia from earning a comfortable 2-0 win on Thursday night.
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