His expensively-assembled side was swept away by an Atlanta side who were three up at half time and could have won by a cricket score.
Afterwards, a stunned Koeman accused his players of lacking passion but insisted the buck stops with him.
And alarmingly, after three defeats in a row, the Dutchman does not have answers to explain Everton’s early-season crisis.
“This was a big lesson and I need to ask myself questions what I did wrong,” said Koeman, who apologised to the 2,200 travelling fans who vented their anger on the final whistle.
“It has been a tough start but this was different.
“What I saw on the pitch was very different from what I want from Everton.
“In the first half we made many mistakes and Atlanta showed the passion and aggression you need to play football.
“It is easy to criticise individuals but the team was not prepared for this.
“You can make excuses but I think most of the players are not at the level we expect.
“It is a difficult moment and a wake-up call. If it isn’t, then the problems are even bigger.”
You certainly don’t get a lot for £130m on this alarming evidence.
This was meant to be Everton’s big season but right now, they look an ill-balanced, hotch-potch of a team with the whole, a pathetic fraction of the sum of its parts.
They were an absolute shambles as Atalanta celebrated their return to European football after 26 years with a win far easier than they could have dared imagine.
