Koeman, who wanted his side to react strongly after a 3-0 Premier League loss to Tottenham Hotspur over the weekend, said he would not blame his players for their latest defeat.
"It is a big lesson tonight," Koeman told the club website (www.evertonfc.com) after Thursday's loss.
"But it is not the time or the place to criticise the players. I have to criticise myself because the team was not prepared for this tonight.
"I thought that was happening after the third goal against Tottenham at the weekend but I need to ask myself the question what I did wrong," he added.
Koeman said he saw a big difference in the belief and confidence between his side and Italy's Atalanta, who returned to European competition after 26 years.
"They had aggression and passion. We made mistakes, the pitch wasn’t the best, either, but it was the same for them. Atalanta showed to us the passion that you have to have when you play football," Koeman said.
Everton must regroup as they visit Premier League leaders Manchester United in the league on Sunday.
United have 10 points from four matches and have scored 12 goals this season while Everton are in the lower half of the table with four points.
(This story was refiled to fix club spelling in headline)
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Amlan Chakraborty)
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