The job was already done before Celtic set foot in the Parken Stadium, which is just as well because Gordon Strachan’s side saved the worst for last as they rounded off their group F campaign with this wretched display.

Copenhagen was far from wonderful for their travelling fans who had to witness yet another defeat on the road that was in stark contrast to the high-octane night in the east end of Glasgow a fortnight ago when Celtic assured themselves of a place in the last 16 with that dramatic victory against Manchester United.

The two British sides will now go into the knockout phase, with Celtic finishing in second place after United beat Benfica 3-1.

Any notions of actually winning the group were removed by Atiba Hutchinson and Jesper Gronkjaer, who put the contest in FC Copenhagen’s control after just 27 minutes before Marcus Allbäck added a third in 74 minutes.

Jiri Jarosik did manage to find the net for Celtic when he ghosted in at the back post to meet Shunsuke Nakamura’s free kick 11 minutes from time and Kenny Miller headed narrowly wide, but it was too little, too late for the Scottish champions.

That elusive first away victory in the group stages of the Champions League never looked likely. Celtic have now gone 12 games on the road without tasting success and Strachan will have to hope that 13 is his lucky number when the draw on December 15 identifies the next trip in February.

The 4,000 Celtic fans who travelled found that Nakamura, the hero of the victory over United, whose goal had secured the place of the Scottish champions in the last 16, had been left on the bench.

His place was taken by Jarosik, the Czech Republic player, while there was a return for Mark Wilson at right back. Wilson broke his foot in the opening game in group F at Old Trafford three months ago but Strachan was keen to freshen up his team and this had been the first opportunity to re-introduce the valued Scotland under-21 player.

A bitterly cold Scandinavian night met Celtic but the welcome for the Dane in their midst, Thomas Gravesen, was equally chilly. The man who made 66 appearances for Denmark has not been forgiven for announcing his international retirement just after joining Celtic from Real Madrid in August.

An indication of that hostility came in the opening minutes when Gravesen clipped the ball into the Copenhagen net from Miller’s cutback — the striker being judged to have just carried the ball beyond the byline — and a hail of jeers erupted around the stadium.

Just 60 seconds later, the ground was in a ferment as Copenhagen stormed into the lead. A throw in from Tobias Linderoth on the right was glanced on by Hutchinson to Allbäck for the Sweden forward to hold the ball up on the edge of the box and return into Hutchinson’s path. The Canadian burst between Bobo Balde and Neil Lennon into the box and steered a left-foot finish beyond Artur Boruc before Wilson could get his tackle in.

That was the response that Stale Solbakken, the Copenhagen coach, had demanded in this final group game at home after defeating United and drawing with Benfica here.

Celtic could have been further behind after 15 minutes only for the underside of the bar to come to their aid. Gronkjaer’s free kick from the left was poorly cleared to the feet of Allbäck and his shot struck the bar and stayed out.

Celtic were being outplayed and knew they had to construct some threat to the Danes before ceding control totally.

Miller came close to restoring parity on two occasions after 20 minutes. Both were created by Lee Naylor. The full-back swung over a fine cross to set up the first chance and that was headed just over the bar by Miller.

Then, the forward seized on another fine pass from his colleagues that unlocked Copenhagen’s defence. Miller raced in behind Brede Hangeland and then rounded Jesper Christiansen, the goalkeeper, only for the vigilant Michael Gravgaard to deny his shot on goal with a slide tackle.

Miller was then through moments later only to be harshly judged to have tugged Hangeland. That decision was compounded in the 27th minute when Copenhagen scored again. Linderoth’s corner was headed back across goal by Hangeland and Gronkjaer conjured up a diving right-foot volley past Boruc.

The Parken Stadium was now in the midst of raucous celebration and Celtic could do little to defuse the mood. Aiden McGeady had a chance when put clear just before half time but Christiansen raced out of his box.

Celtic needed a response early in the second half if they were to regain any hope of making a comeback. They thought they had found what they were looking for in the 53rd minute when a run by Jarosik took him past three tackles before feeding Maciej Zurawski on the edge of the box. The striker’s raking shot was parried away by Christiansen and though Miller looked poised to seize on the rebound, the goalkeeper regained the ball.

Four minutes later, Copenhagen had stretched their lead. A free kick was awarded in the centre circle after Michael Silberbauer, who was not looking, turned into Balde.

Linderoth delivered the kick and this time Gravgaard climbed higher than his markers and glanced the ball down into the run of Allbäck for the striker to steer an angled right-foot shot beyond Boruc, who was complicit with his defence in the appalling lack of communication.

Strachan looked on from the dugout in bemusement. He stood impassively for almost ten minutes before sending in Stephen Pearson and Nakamura for McGeady and Gravesen to try to rescue some pride.