Own goals from Aimar Tárrega and Mouctar Diakhaby either side of an Aubameyang strike put Deportivo firmly in control, with Umar Sadiq's finish before the break offering only brief hope for the visitors.
Asked directly whether he felt shame at the performance, Corberán did not equivocate.
"Impossible to take anything positive, because it was a match, especially in the first half, that was shameful - one we cannot accept," he said. "We have not been the competitive team we had been, and we were not at the level that competing in a football match demands."
The Valencia boss placed the blame squarely on collective attitude rather than individual errors.
"Above the individual mistakes, I think we didn't come out with the necessary attitude to compete in a match," he said, tracing the warning signs back to before Deportivo's opening goal.
"We were switched off before the corner, having already conceded four corners. The first few minutes were dreadful because we never got into the game. When you don't enter a match the way you have to, any team can put you to the sword, which is what happened."
Pressed on whether Valencia's issues ran deeper than attitude, with the transfer window closing and an injury list mounting, Corberán refused to shift the conversation towards the market.
"Above any question about the transfer window, what we have to do today is compete at the level we're capable of, and today we didn't do that, which is why we lost," he said.
Asked what he would ask of the club with the deadline approaching, he turned the responsibility back on himself.
"After a match like today, I'm in no position to demand anything of the club. I can only demand that I do things better, because I am not representing Valencia the way I should."
He closed with an apology to the roughly 400 Valencia fans who had travelled to Riazor.
"Unfortunately, today we can only apologise."
Deportivo boss Antonio Hidalgo, by contrast, savoured a first win since the club's promotion back to the top flight.
"It's very nice to get my first win as a coach in the top category," he said, praising his own supporters as "the best in Spain."
"It was written that they would start singing and cheering from the 12th minute - and that's exactly the minute we scored. We're powerful together."
Hidalgo was pleased with his side's defensive control.
"We've conceded very little, which leaves me calm about the performance we put in with and without the ball. These are three very important points, and now we have to think about Villarreal."
The one area for improvement, he noted, was recent defensive errors from two young players, Lucas Noubi and Bright Ede.
"They're very young lads, on an accelerated course in how to play in the top flight."