Celtic had Jeremy Toljan sent off in the first half as they were eliminated from the Europa League in a 1-0 defeat at Valencia on Thursday, losing 3-0 on aggregate.
Goals from Denis Cheryshev and Ruben Sobrino in Glasgow had left Celtic with a mountain to climb at Mestalla and Toljan's two bookings made their challenge even greater.
The Scottish champions worked hard but with little success and Valencia - with their two-goal and one-man advantage - made sure of their progress through substitute Kevin Gameiro in the 70th minute.
Celtic defender Kristoffer Ajer had two bites at the cherry from a corner in the 10th minute, seeing one attempt blocked before his second was blasted over.