Kuban needed to win against the already-qualified Spaniards while also making up three goals on Swansea to stay alive in the competition, and the Swans gave the Russian side every opportunity by losing meekly at bottom side St Gallen in the night's other match.
However, Kuban failed to get the get the job done at the Mestalla, with Lorenzo Melgarejo's late equaliser that cancelled out Paco Alcacer's opener all they had to show for their efforts.
Valencia finish top of Group A on 13 points, five clear of Swansea who join them in the last 32.
Valencia were the first to threaten when Michel hit the post from close range in the 21st minute, while moments later Michel's inswinging corner was headed over by Helder Postiga.
Neither side offered much as an attacking force in the rest of the half and almost an hour had gone when another chance came along, Kuban's Djibril Cisse bringing a smart stop from Diego Alves.
The breakthrough arrived on 67 minutes when Ever Banega played in Alcacer who tucked the ball home from six yards to put Valencia on course for their fifth win in five games since their matchday one humiliation at home to Swansea.
But Kuban ensured Valencia would drop points for only second time in the group when they levelled six minutes from the end when Gonzalo Bueno crossed and Melgarejo headed high into the net.
There was still time for a little late drama when Valencia's Victor Ruiz was sent off for a professional foul on Cisse in the final minute, but Kuban were unable to capitalise.