"It's a huge step back in terms of winning La Liga," Koeman lamented in his postmatch news conference. "It's disappointing but we must accept it, even though being 12 points back from a strong team like Atletico is a lot.
"The result today is difficult to explain. We concede the first goal and weren't good in attack, with too many players in the middle of the pitch.
"That's not the level I expect from my team. We must improve. We must be more focused. In general, the attitude without the ball was not good."
"Our throw-in ends up in a goal for them," added an angry Koeman. "It's our mistake. It's incredible and you don't expect it from our team. You cannot concede a goal like that.
"I think it's a lack of concentration. We lack aggression without the ball. That could be why. It's not easy to explain how we concede that second goal. It's very disappointing."
Barca have now fallen behind in six of their 10 league games this season and have failed to win any of them, drawing two and losing the other four.
"It's worrying to lose so many games," midfielder Sergio Busquets told reporters. "The more we slip up, the further we are away from the top, which is where we want to be.
"I think individual mistakes have cost us a lot of points and we can't keep giving the opposition that early advantage.
"Once we're behind, it enables teams to shut up at the back and deny us space. It's not a question of attitude or commitment, but starting games like this makes it much more difficult."