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Antoine Griezmann and Alvaro Morata both scored twice as 10-man Celtic suffered a bruising loss at Atletico Madrid to remain rooted to the bottom of Champions League Group E.
Daizen Maeda was sent off after a booking was reassessed via the monitor, with the visitors trailing to Griezmann's early deflected strike.
Morata added a close-range finish before the interval and thundered in the fifth after great efforts from Griezmann and Samuel Lino, while Saul scuffed in the sixth.
With two games remaining, Brendan Rodgers' side are five points adrift of Feyenoord in third place.
Atletico lead the way on eight points, one ahead of Lazio, who Celtic visit next.
Celtic's solitary point came against the Spanish side in Glasgow a fortnight ago. That was a thrilling contest with no quarter given. This was a mundane, one-sided affair by comparison, given the visitors' miserable start, although there was much to admire in the hosts' ruthlessness and fine finishing.
The game completely raced away from Celtic as Diego Simeone's team seized on their personnel advantage, which came after referee Ivan Kruzliak was asked to review the yellow card he had given Maeda for catching Mario Hermoso on the shin.
The harsh red card played a massive part, but the nature of the opening goal will also frustrate Rodgers, given Celtic had started brightly.
It felt both key and avoidable as Callum McGregor nodded into a dangerous area outside the box. That was compounded by it landing at the feet of Griezmann, who sent in a shot that cruelly diverted beyond Joe Hart.
Celtic's response was initially strong. They held onto the ball well and Maeda, in particular, caused problems down the right. That threat came to an abrupt end when he went into a challenge with a raised boot, Hermoso went down and the Atletico players, on the pitch and on the sidelines, reacted with animated fury.
Rodgers was incensed by counterpart Simone's role in the protests as the yellow card was upgraded to red.
Morata's strike just before half-time ended Celtic hopes as he slid in to meet Jose-Maria Gimenez's nod across goal.
The Spanish side were utterly merciless from that moment, oozed quality and scoring some exceptional goals.
Griezmann's second, an overhead kick, was brilliant giving Hart little chance.
Substitute Lino more than matched that when he bent a lovely shot into the far corner.
The trend continued when Morata crashed in a swerving fifth from the edge of the penalty area and a late sixth arrived when Saul poked home.
In truth, it could have been more with both Angel Correa and Gimenez denied by the woodwork in a torrid second half for Celtic.
Griezmann was brilliant throughout. He is a player a the top of his game and was central to everything Atletico Madrid did. His second goal was outstanding.
With 11 players, Celtic might have suffered against this side. With 10 it was impossible. It all fell apart after a promising opening. Maeda's dismissal, Celtic's third in this campaign, was a hammer blow against opposition who showed incredible hunger to chase goal after goal.
Rodgers was upset by the decision but will also be unhappy with some of the defending at crucial moments. That said, some of Atletico's goals were truly exceptional. Their work-rate, tactics and execution were top class as Celtic's night went from bad to worse.
A painful setback after signs of improvements at this level.
Celtic manager Brendan Rodgers: "It's a huge gulf, you see that. These players gave everything. The sheer quality of Atletico overrides our effort.
"I feel for the players. We were undeserving of the red card, and when we get it, it's a huge challenge.
"When you see the images that the referee has seen, it wasn't representative of the actual challenge.
"I don't want to go on about the officials. You have to accept decisions. It feels more like a computer game, the constant looking at the screens."
Atletico Madrid forward Antoine Griezmann: "We started the match really well and not doing that is something that has cost us before. Then the sending off gave us calmness, more space to play in. The team has played a really good game, we need to continue like this."
