CELTIC have certainly not have kissed auf wiedersehen to their hopes of being involved in European football beyond Christmas despite this sobering defeat at the hands of Bayern Munich in Germany last night.

With Paris Saint-Germain trouncing Anderlecht away as expected they remain in third place in their section with three games remaining and dropping into the Europa League in the new year remains an achievable objective.

Yet, their prospects of coming second in Group B and progressing to the knockout stages of the Champions League for the fourth time in their history appear next to non-existent after being outclassed and soundly beaten in this outing.

Read more: Brendan Rodgers defends tactics after Bayern Munich defeat and insists Celtic can still progress in Europe​

It had been suggested by some optimists among their fan base that they could possibly emulate the achievements of their predecessors in the 2006/07, 2007/08 and 2012/13 campaigns and finish ahead of Bayern following their 3-0 win in Belgium last month.

But Jupp Heynckes’s charges, who triumphed easily thanks to first-half goals from Thomas Muller and Joshua Kimmich and a second-half strike from Mats Hummels, showed they are operating at a far higher level to Brendan Rodgers’s men here.

The Scottish champions have two home games to go and their supporters will rightly point to the many big names, not least Barcelona who they defeated on the last occasion they reached the last 16 of this competition, they have humbled in the past.

However, this encounter provided further evidence of the ever-widening gulf between the superpowers of continental game and those from lesser football nations. The margin of victory would have been far greater had Craig Gordon not saved well from Robert Lewandowski, Kingsley Coman, Arjen Robben, Muller, Thiago and substitute Arturo Vidal.

Read more: Bayern Munich v Celtic: How the players rated

To lose by such a heavy scoreline against such formidable opponents away from home was hardly surprising and was by no means shameful. In their previous 10 games in this competition at home Bayern had won all 10, scored 33 goals and conceded just two. Far bigger and better clubs than Celtic will suffer the same fate at this quite magnificent venue. But it was a stark reminder of the level both of the combatants are now operating at.

Rodgers, as expected, moved Mikael Lustig in to centre half in the absence of the injured Jozo Simunovic and handed Cristian Gamboa a start. It was hardly ideal given he had only played his first game at club level and his third game this season at the weekend.

The options available to the Celtic manager, however, were hardly plentiful. He clearly felt safer bringing in another specialist defender than playing midfielder Nir Bitton out of position with Lewandowski playing up front for the hosts, Muller sitting just off him and Coman and Robben out wide.

Gamboa, a Costa Rican internationalist, made his debut for the Scottish champions in equally demanding circumstances. He started in the record 7-0 defeat to Barcelona in the Nou Camp last year. He went about his task manfully and made some decent tackles. But he was to endure another dispiriting night.

Read more: Party over as Bayern Munich expose Celtic's defensive shortcomings​

Rodgers had urged his men to take the game to their hosts and they certainly tried to do exactly that. Scott Sinclair, Patrick Roberts and Leigh Griffiths all had their chances in the opening 45 minutes. But their forays into the opposition half amounted to little. They were dispossessed with ease.

Kieran Tierney had their first shot at goal early in the second half and that was easily gathered by Sven Ulreich. Scott Sinclair, Tom Rogic and James Forrest all forced good saves from the keeper after that. But by that stage in proceedings the game was well won.

Celtic’s distribution of the ball from the back frustrated Rodgers, who paced around his technical area for the duration of the 90 minutes, at times, when his players were not being placed under any pressure especially. But it would have made little difference if it had been been better such was the total superiority of their rivals.

It took just six minutes for the home team to find the net. Fortunately for the away side, assistant referee Tikhon Kalugin spotted that the ball had gone out before Lewandowski had cut it back to Thiago and it was disallowed. It did not take long, though, for them to forge in front.

Read more: Brendan Rodgers defends tactics after Bayern Munich defeat and insists Celtic can still progress in Europe​

Kimmich dinked the ball over the heads of the Celtic defence in the 17th minute, Lewandowski beat the offside trap, ghosted past them and directed a downward header at goal. Craig Gordon showed fine reactions to deny him with a one-handed save. But Muller pounced and rifled into the roof of the net.

Kingsley has been raising smiles in Scottish football circles since Partick Thistle unveiled their David Shrigley-designed mascot two years ago. The presence of his namesake Coman failed to provoke a similar response in the man charged with marking him last night.

Coman danced past Gamboa to set up his side’s second goal in the 29th minute. He chipped the ball back from the byline and found Kimmich whose header was perfectly weighted. It arched into the top left corner.

Hummels met a Robben corner with a sublime glancing header in the 51st minute to put Bayern three ahead and round off an emphatic victory.

Read more: Bayern Munich v Celtic: How the players rated

Rodgers threw on Moussa Dembele for Griffiths, Rogic for Armstrong and Forrest for Roberts. His replacements made little difference. Sinclair curled the ball into the goal in the 86th minute to the delight of the 4,000 or so away fans high up in one corner of the 75,000 capacity stadium. But his effort was correctly adjudged to be offside. Lustig also headed onto the post at a Rogic corner in injury-time.

Remarkably, Bayern were understrength last night. How good will they be in the new year when Javi Martinez, Manuel Neuer and Franck Ribery, who are all out injured, are available? They must surely be considered contenders to win this competition for a sixth time this term.