Everton fell victim to a 3-0 defeat on Thursday night, after a dismal performance saw them lose their opening Europa League game to Atalanta.
Koeman's side went 3-0 down to the Italian side in the first half and didn't really make a go of it all game, creating very few clear cut chances in a dismal performance.
Atalanta - who are playing in just the fifth European tournament campaign in their history - impressed, but Koeman acknowledged that his side made a lot of mistakes on the night.
"A lot went wrong, except maybe after a difficult start, maybe 10 minutes that we had a little bit more of the ball and looked a bit more comfortable," Koeman told BT Sport after the game, via TalkSport.
"Ball possession was poor, but most painful was in the first half that they showed more aggression, that they showed more passion and that's really painful because in my opinion it starts with that and then you need qualities on the ball."
"It's a good question to the manager, because I asked myself the question 'what am I doing wrong?' about the second half against Tottenham, and the first half, because it's the way I like to see my team."
"We can play better football, missing chances to score, but the commitment, the passion that they showed to us in the first half was much bigger than we showed together."
"We knew from the beginning of July that the start of the season was really tough. Okay, we need to accept it, but that's not the problem. The problem is what we showed in the first half together."
Everton will travel to table-topping Manchester United in their next game, in a difficult fixture where if Koeman's side get embarrassed again the pressure may well start to build on the Dutchman.