The 59-year-old coach said it is the worst performance he has seen all season, but took responsibility for the defeat.
"Osasuna deserved to win," Herrera told reporters. "We haven't played well at all.
"To be honest, it's the worst I've seen us play all season. There are no excuses for a performance like that. That was not my usual team out there – I'm worried and quite upset with what I saw. As the coach, I am responsible.
"I found it genuinely uncomfortable to watch. The first half was appalling – at half time I asked them to lift their heads and go for it. And we didn't do that."
Os Celestes welcome Valencia to the Balaidos on Saturday.