Please Wait . . .
Defeat – their third in a little over a month – means they could end the weekend in the bottom half of the table, with the Blaugrana seemingly struggling to recover from a tumultuous pre-season off the pitch.
The solitary goal conceded against Atletico came at the end of the first half when Gerard Pique – who was later substituted with anasty-looking knee injury – failed to cut out Angel Correa's pass, and Yannick Carrasco skipped past the stranded Marc-Andre ter Stegen before slotting into an empty net from 35 yards.
The whole situation left Koeman frustrated.
"It is worrying," he told Movistar . "For a big team, conceding a goal like this ... it can't be, because it's the 47th minute, we had the ball and then they score, 1-0.
"We controlled and we knew that it was difficult to create many chances. We had a pair and with the score 0-0, the game would have been totally different if they had taken either chance.
"Like any coach, I am responsible for the team's results."
Although the campaign is still in its early stages, Atletico's win sawthem go nine points clear of Barca.
Koeman recognised it as a significant gap to bridge and is demanding a streak of wins from his men in response.
"It's a pretty big difference, but there is a lot of the league left and a lot of games," he continued.
"We know that every match is complicated, but after this defeat we have to chain an important winning streak.
"I have seen a team that has fought until the last second to been able to level the game, so in this sense I am not worried."