After being pipped by Barcelona then beaten in Marseille, Andy Welsh’s lads simply had to win this tie to have a hope of squeezing into second spot and making the New Year play-offs.
Instead they were left rock bottom of a fiendish Group One, with the suprisingly slick Glasgow outfit breaking their own duck in weather more suited to ducks than playing constructive football.
City started well enough, and took the lead after ten minutes, although they had plenty of help from the visiting defence as the conditions caused some measure of havoc.
Harry Bunn swept past Michael Miller down the left and fired in a workaday shot that Robbie Thomson saved, but he spilled the ball and skipper Marcus Fraser couldn’t clear his line quickly enough.
Joan Roman took the initiative, nipped in smartly and poked the ball over the line to put the Blues in a perfect position so early in the game. Unfortunately, it wasn’t to last.
Celtic had pace and not a little skill, and a couple of minutes later Calum McGregor fired a warning with a fierce shot that Gunn managed to tip against his left-hand post.
The Scots pulled level after 25 minutes, and again there was a real element of poor defending in the goal as City skipper Karim Rekik stranded his keeper with a poor back pass to allow John Herron in.
Celtic had a grip on the game by now, and the Blues were under pressure as the wind and rain made defending ever harder
The visitors looked to have a good penalty shout turned down when Tony Watt went sprawling under a challenge from Ellis Plummer.
That was after 38 minutes. A minute later Celtic were ahead with a powerful header by Paul George from a corner, and in all fairness City could not complain given the way Celtic had played.
Worse was to come for the Blues, who replaced defender Plummer with Luke Coulson at half time, as George shot Celtic further ahead just before the hour mark.
The credit went to Dylan McGeouch, who took possession from a short corner then weaved through City’s defence on the right flank before setting up George at the near post.
The Blues refused to let their heads drop though, and Dennis Suarez and Roman conjured the goal of the game to briefly resurrect their hopes after 65 minutes
Suarez was the instigator with a surging run from midfield, then his one-two with Roman allowed the Spaniard to penetrate the area and curl a lovely left-footer round goalkeeper Thomson.
But Celtic were not to be denied, and three minutes later a breakaway ended with George setting up Watt to fire across Gunn for a fourth goal that left City with too much to do.
Roman tested Thomson with a free kick that the Celtic keeper was happy to punch clear, but there was no arguing that the Scots had been the more resilient and incisive on the night.
Welsh said: “We’re obviously disappointed . At this level we have to defend better than that. We have to be brighter and sharper. But we have to be positive and learn from this.”