Carrasco showed a cool head to roll into an empty net from over 30 yards out after goalkeeper Marc-Andre ter Stegen was caught well off his line.
Clement Lenglet came closest to equalising for Barca, who lost Gerard Pique and Sergi Roberto to injury, but Atletico held on to maintain their unbeaten record in the league and move level on points with leaders Real Sociedad.
Koeman will come away from the Wanda Metropolitano with a long list of negatives and few positives. At a push, Ousmane Dembele's renewed resilience is good news for Barca and the France forward could play an increased role in the coming weeks.
Before even analysing the performance, Barca will be fearing the worst after Pique left the pitch with a knee injury. With Samuel Umtiti and Ronald Araujo also injured, Lenglet is the only fit centre-back at the club at the moment. Losing Pique for any length of time would be a disaster and, well, it doesn't look good.
To make things worse, Sergi Roberto also limped off late on, although his injury didn't seem as serious.
However, Barca cannot blame injuries for Saturday's defeat. This was a toothless performance that lacked leadership and they struggled to break down Atletico. They created hardly any chances and, at the risk of disturbing the elephant in the room, Lionel Messi is a long way from his best.
Manager rating (out of 10)
5 -- Koeman was already without Sergio Busquets and Ansu Fati due to injuries so could ill afford to lose more players. In that sense, in terms of personnel, he had his hands tied at the Wanda. However, it's still fair to ask for him to be a little more creative with his tactics. This is still a Barca side with attacking players like Messi, Dembele, Antoine Griezmann and Philippe Coutinho in the ranks. Finding a more effective combination is vital.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Marc-Andre ter Stegen, 5 -- Made a brilliant save from Saul Niguez in the fifth minute but carries the lion's share of the blame for the Atletico goal. Was caught out miles from his goal when vainly trying to intercept the long pass forward, and Carrasco took full advantage.
DF Sergi Roberto, 6 -- Did OK at right-back and worked hard when pushed into midfield, but his mediocrity is a sign of how the standards have slipped at Barca.
DF Gerard Pique, 5 -- Made a mistake leading to the Atletico goal on a night he'll want to forget in a hurry. Was close to tears when he left the pitch in the second half injured.
DF Clement Lenglet, 6 -- Had two of Barca's best chances, both headers. The second was their best chance, but he nodded straight at Jan Oblak.
DF Jordi Alba, 6 -- Got into a couple of promising positions on the left and set up one good chance for Messi.
MF Miralem Pjanic, 6 -- Came in for the injured Busquets and did enough to keep his place. Good on the ball and an alternative to Messi at set plays.
MF Frenkie de Jong, 6 -- Barca need more from him in midfield, but he continues to do well when asked to play as a makeshift centre-back, something that's sadly happening far too often.
FW Ousmane Dembele, 7 -- Was lively early on and created a good chance for Griezmann inside the first five minutes. Looked like he would beat his man every time he got the ball at one point, but Atletico did eventually get to grips with his pace.
FW Lionel Messi, 6 -- Will look back on his chance just before the first goal, set up by Alba, when he shot straight at Oblak. Also created Barca's best opening for Lenglet. Despite that, still looks nowhere near his best.
FW Pedri, 6 -- A quiet game on the left after a flurry of impressive performances in recent weeks. Struggled with Atletico's physicality.
FW Antoine Griezmann, 5 -- Unable to deliver against his former side. His best chance was a header straight at Oblak just before he was taken off late on.
FW Philippe Coutinho, 6 -- Returned from a hamstring injury to little effect in the second half.
DF Sergino Dest, 6 -- Replaced the injured Pique and offered an outlet on the right in the final quarter of the game.
FW Martin Braithwaite, N/R -- Thrown on late on and had one dipping shot blocked.
FW Francisco Trincao, N/R -- Some nice footwork in limited minutes, but his showmanship led to nothing.