It was a crushing, comprehensive defeat – Arsenal’s joint heaviest in European football and one that appeared to severely dent their prospects of Champions League progress.

Reflecting on their 5-1 hammering by Bayern Munich, Gunners boss Arsene Wenger readily acknowledged that the odds were now weighted against his side successfully securing a last 16 berth.

“It’s a small chance but it is a real one,” declared Wenger. “With that kind of performance we had, our chances are minimal. No matter what percentage we have, we have to dig in for the chance to qualify.”

While the psychological scars of that thrashing in Bavaria may yet have done irreparable damage, the result itself actually has little bearing on their prospects.

Even had they secured any kind of positive result against the German champions, the scenario facing Wenger’s side would still have been the same – the requirement to defy history and win their final game, away to Olympiacos.

Arsenal have lost all three of their previous Champions League away encounters with the Athenian club, each of them within the last six years and always the final match in the group stage.

However, none of those defeats cost the Gunners a place in the knockout stages, whereas their next trip to Greece in December will certainly spell doom if they fail to win.

That, of course, is assuming that Arsenal are still in contention following their home clash with Dinamo Zagreb on November 24 – with the losers of that match condemned to elimination.

The winners would also be out if Bayern’s game against Olympiacos the same night were to finish in a draw. However, their form so far in Group F suggests the German champions are more likely to win and secure top spot.

So it’s by no means far-fetched to imagine that Arsenal could triumph against Zagreb and head for Athens needing victory by two goals to edge out their hosts for the runners-up spot.

It could happen. But that hypothesis is far less likely to become a reality if Wenger has failed to heed the lessons of the Gunners’ 3-2 home defeat to Olympiacos earlier in the campaign.

Goalkeeper David Ospina shouldered most of the blame after spilling a Kostas Fortounis corner over the line to gift the Greek side a 2-1 lead on that miserable night at the Emirates.

But the real problem was not Ospina’s performance, but his selection that night. The fact that first-choice keeper Petr Cech was left on the bench by Wenger sent a clear message to Arsenal’s opponents.

So did the manager’s decision to leave out other regular starters such as Per Mertesacker, Nacho Monreal and Aaron Ramsey. It told Olympiacos, very clearly, that Wenger didn’t think he needed to pick his best players to beat them.

That surely helped to fire up the Greek side, spurring them to achieve their first ever success on English soil.

Wenger’s excuse was that squad rotation was essential because of the heavy schedule his players faced. But even if that were so, why did he choose to give certain individuals a break in that game – where the earlier defeat in Zagreb had already made victory essential?

Surely Arsenal’s Premier League fixture at Leicester three days earlier would have been a better opportunity to make changes.

Wenger might well claim that Leicester’s unexpectedly strong start to the season dissuaded him from such a course of action – but he then underestimated Olympiacos. He is certainly unlikely to do so again when their final Group F fixture comes around.

That December 9 clash – interestingly, the exact anniversary of their 1-0 loss to Olympiacos six years ago – is sandwiched between the Gunners’ home game against Sunderland and a visit to Aston Villa.

On the basis of the current table, Villa and the Black Cats are the two worst teams in the Premier League. They are not title rivals, they are sides Arsenal should be confident of beating.

And yet… if Wenger’s side fail to win one or both of those games, so be it. They will still have more than half the league campaign remaining in which to make amends.

That will not be the case in the Champions League. If they get a chance to qualify in Greece, Wenger must go all out and seize it by selecting the strongest side he can, simple as that.

Munich should already be a distant memory. That game was never likely to decide Arsenal’s European fate this season. Olympiacos, on the other hand, probably will.