The Hoops required at least a point against the visiting Spaniards to stay in the hunt but were unable to peg back Arda Turan's 30th minute opener to fall three points behind the top two in Group I.
Neil Lennon's men had the ball in the back of the net through half-time sub Gary Hooper but an apparent handball from Anthony Stokes denied the equaliser just after the hour-mark as Celtic tried to find a way through but could not breach Chelsea loanee Thibaut Courtois' goal.
Another worry for Lennon was the injury sustained by winger Joe Ledley who was stretchered off prior to half-time and had to be replaced by Charlie Mulgrew.
The Hoops will now have to beat Italian club Udinese on match-day 6 on December 15 in Udine to replace them in second place to progress from the group stages with Atletico already through. The fact that the Glasgow giants have saluted just once in their past 10 away outings in Europe makes this a very difficult task indeed.
Yellow cards:CEL - Daniel Majstorovic 54', Ki Sung-yeung 58' ATL - Gabi 60', Miranda 66', Luis Perea 71'