Felipe Melo swooped for Almeria's winner early in the first-half and soon the boos and whistles were raining on Valencia's already shell-shocked players.
Koeman's men have not registered a win in the last nine games and the Dutchman said at the final whistle: "The culprit is the trainer and I accept that. I am not the person in charge of the decisions that were taken, the team is as it is.
"The situation is worrisome and now I must look at everything up and down. Like everybody, I also commit errors. I will never tender my resignation, not today nor Wednesday nor at the end of the season.
"This club is in crisis and we can only fix this on the field. It is not necessary to look for the guilty, but we are struggling."