Celtic entered this match knowing they had a mammoth task at hand, with no wins in their last six Champions League away games, and having kept just one clean sheet in their last 34 games in the competition.
Atletico Madrid got off to a perfect start taking the lead inside six minutes.
A cross into the Celtic box was headed away to the feet of Antoine Griezmann, who was lurking on the edge of the danger area and his deflected shot deceived Joe Hart, nestling into the bottom corner.
The Hoops looked to be growing into the game after falling behind and thought they had a penalty on the quarter-hour mark after Daizen Maeda was entangled with Mario Hermoso when travelling with the ball into the box.
A VAR review found that the contact happened outside of the box, therefore resulting in no spot kick.
The two were involved in an incident minutes later as the Japanese forward went in studs up dangerously onto the leg of Hermoso, resulting in a yellow card initially, but after rewatching the pitchside monitor, the referee upgraded the card to a red - their third in the Champions League this season.
Their task was made almost impossible right on half time, as Alvaro Morata prodded the ball home after Jose Maria Giménez headed across the face of goal.
The home side were relentless after the break, producing a barrage of chances as Celtic were desperately clinging on.
Gimenez struck the crossbar with a looping header, before Griezmann put the game to bed with a superb acrobatic finish after the visitors failed to deal with a cross into the box.
Atleti were in the mood for goals and added a fourth just after the hour-mark.
This time, Samuel Lino picked up the ball on the left wing, jinked into the box and let a sublime curling finish into the far corner.
Simeone’s Atleti side quite rightly have a reputation of grinding out 1-0 victories, often with football that many would say is not pleasing on the eye.
Their fifth goal, however, was the complete opposite, as a 24-pass move was finished off by Lino chesting the ball towards Morata on the edge of the box and the Spaniard took a touch and then rifled the ball into the top corner - a beautiful team goal, summing up their dominance on the night.
The Spanish outfit added a sixth goal late on as Saul Niguez pounced onto a loose ball, firing into the roof of the net and they sit atop of Group E with two games remaining, whilst Brendan Rodgers’ Celtic look destined to exit Europe after a disappointing campaign, with just one point after four games.
Flashscore Man of the Match: Antoine Griezmann (Atletico Madrid)
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Lazio leapfrog Feyenoord
Meanwhile, Lazio leapfrogged Feyenoord in the group with a big win.
Their narrow victory put the Italian side on seven points, one ahead of Feyenoord and one behind Atletico Madrid, who still have to face both of their rivals.
Lazio and the Dutch champions are both all but certain to finish third and go into the Europa League at the very least, with Celtic six points behind the former and five behind the latter.
