The visitors were still warming to their task when Colombian striker Radamel Falcao met a Diego corner in the third minute to head past Hoops keeper Fraser Forster.
Diego added the second in the 67th minute to leave the Parkhead men with one away win in Europe in 31 games ahead of Sunday’s Old Firm clash at Ibrox.
Celtic were reinstated in to the competition after Sion, who beat them 3-1 on aggregate in the play-offs, were thrown out by UEFA after being found guilty of fielding ineligible players.
Neil Lennon may have wished they had not bothered, though, with a beating in Madrid not the ideal preparation for an Old Firm clash at Ibrox on Sunday.
Lennon made three changes, with right-back Mark Wilson replacing Adam Matthews while stopper Glenn Loovens came in for cup-tied Badr El-Kaddouri and Charlie Mulgrew moving to left-back.
Georgios Samaras took over from Anthony Stokes, who missed the trip to Spain with a thigh injury.
It was a nightmare start for Lennon’s side, who had conceded a penalty and a goal in the first minute in their 3-1 defeat in Sion.
The game was barely into the third minute when Mulgrew conceded a corner and Diego’s cross into the box was met by Falcao who bulleted his header from 10 yards past Hoops keeper Fraser Forster.
Celtic wobbled in the following moments but in the sixth minute lone striker Gary Hooper was set up by stand-in skipper Beram Kayal.
Atletico keeper Thibaut Courtois rushed from his goal to block the former Scunthorpe striker’s close-range shot.
The visitors composed themselves and certainly posed a threat when they went forward but Atletico also looked dangerous any time they encroached on the Celtic penalty area and in the 13th minute Diego had an effort from 25 yards which flew wide.
The home side began to impose themselves and Mulgrew did well to block a goalbound header from Falcao at the expense of a corner before Arda Turan fired in a shot from distance which went too close to the visitors’ goal for the comfort of Forster.
Lennon’s men were finding it difficult to get out of their own half at times and in the 33rd minute Forster had to make a decent save when Turan unleashed a shot from 25 yards.
Celtic began the second half positively when midfielder Ki Sung-yueng’s powerful drive from 30 yards had to be tipped over the bar by Courtois although the corner came to nothing.
There was a penalty claim at the other end moments later when Parkhead midfielder Joe Ledley tangled with Diego in his attempt to thwart a strike on goal but Danish referee Peter Rasmussen was unimpressed.
Former Arsenal star Jose Antonio Reyes replaced Koke in the 56th minute as Atletico looked to get back into their stride which by this time looked to have been broken by some spirited battling by Celtic.
Atletico midfielder Mario Suarez was rightly booked for a cynical foul on Samaras in the 58th minute as the former Manchester City striker broke with purpose over the halfway line.
In the 65th minute, after Arda Turan had bundled Ki to the ground 30 yards from goal, Mulgrew came close with his free-kick, the ball speeding just past the near post.
But in the 67th minute the home side doubled their lead in quite simple style after they had cut open the Hoops defence with Turan’s cut-back placed confidently in to the net by Diego from 12 yards.
The goal sapped belief from the visitors and soon afterwards Forster had to make a great stretching save from Turan who had been set up by Antonio Lopez.
Ledley and Kayal both had efforts which missed the target as Celtic tried to fight back but it was way too little too late and once again the Parkhead side were left to ponder a night of failure on their European travels.