The best chance of Marcelino's side getting back into the Champions League now appears to rest on them overcoming Arsenal in the Europa League semi-finals and going on to win the trophy, which offers the victors a place in Europe's premier club competition.
Brazilian veteran Charles, 35, pounced on a poor attempted headed clearance from Valencia defender Jose Gaya to calmly stick the ball into the far corner of the net in the second of three minutes of stoppage time.
The Basque side had more chances in the first half but Valencia went all out for a winner in the second and strikers Rodrigo and Kevin Gameiro both spurned clear opportunities before Eibar caught Marcelino's side out on the break.
Eibar's last-gasp victory lifted them up to ninth place in the standings on 43 points after 35 games.
(Reporting by Richard Martin; Editing by Toby Davis)
