Who knew Russia chilled in winter?

The artificial heat in Zenit St Petersburg’s closed roof stadium might have masked Celtic from the harshness of the elements but there was nothing that could protect them from the icy blast of reality as the door to football’s Siberia swung open.

No amount of short-sleeved bravado could camouflage the reality of what was a depressingly familiar narrative as Celtic’s involvement in European football this season stuttered to a grim conclusion.

Read more: 'Courage and belief' missing as Celtic crash out of Europa League

Not since 2004 have the Parkhead side found themselves in a position where they have been able to compete beyond this stage in any European competition.

There is an argument, evidence based, that the disparity in resources between the haves and the have-nots ensures that this will be a perennial plotline.

And yet what was so frustrating for the Parkhead side last night was their own part in the downfall; sleepy defenders, a goalkeeper caught wrong-footed, a fragile performance lacking in belief, shape, confidence and cohesion.

As an overall display, it was the converse of the pulsating first-leg in Glasgow. How Celtic must have had cause to rue the chances they passed up when they had their boot on the chest of Zenit last week.

Read more: Celtic keeper Dorus de Vries insists he was not to blame for Zenit's 'nightmare' second goal​

That Roberto Mancini’s were entirely more fluent than they were in the first meeting between the teams was no real surprise. What did raise an eyebrow was just how flat Celtic were in contrast to the richness of that display.

Where there was energy and aggression, there was only meekness, visible from the opening minutes. There was an instinctiveness in how Zenit scented and exploited it.

Jozo Simunovic was culpable when he allowed Branislav Ivanovic a free header and an easy goal, a gift that was destructive in so many ways. The obvious alteration to the balance of the tie so early in the game put Celtic on the backfoot and that unease rippled through the entire team, putting them firmly on the backfoot. They never found a way off it.

Where last week Scott Brown was able to dictate the tempo and pull the strings in the middle of the park, his influence in the game was smothered. Forced to sit deep, the midfielder was never able to get on the ball and offer any real foundation for Celtic to build on.

Read more: Zenit 3, Celtic 0: Scots crash out of Europa as same old mistakes blight European campaign

The talisman for the Parkhead side so often this season, the nullification of Brown was instrumental in muffling Celtic. Rodgers’ side could not, to adopt the vernacular of the dressing room, get in the faces of Zenit the way they did last week on their own turf.

That imbalance seeped all the way through the performance. Brown and Moussa Dembele exchanged words shortly before the break, the frustration of each obvious in the brief altercation. Dembele seemed so static at times that he seemed frozen to the spot. In fairness to the French striker, there was little service that came his way but he was badly off the pace.

Dorus De Vries should and could have saved the cheap second but by the time Daler Kuzyayev had rippled the net to allow Zenit to put their noses firmly in front there seemed to be a grim acceptance of their fate from Celtic. In truth, the whistle could have gone then such was the seal on Celtic’s night.

The stats at the break should that Brendan Rodgers’ side had their fair share of possession but what they didn’t show was where that possession was.

From side to side, Celtic could shuffle the ball about but they just couldn’t find any real penetration. It went sideways, it went back. It rarely went forward, a fact underlined by the lack of a shot on target until the 67th minute – by which point Celtic were 3-0 down - when Olivier Ntcham sent a shot straight down the middle of the goal.

Read more: Celtic v Zenit: How Brendan Rodgers' players rated​

That third had been the evening in microcosm. A move that started from the middle of the park caught Celtic flat and as Simunovic aimed a wild swipe in the box, the ball was directed to the back post where Mikael Lustig, concentration gone, was guilty of allowing Aleksandr Kokorin to sneak in at his back for an easy tap in. For a player of the Swede’s influence and experience, it was an appalling goal to lose.

When the draw was made in December, few would have expected Rodgers’ side to prevail against the Russians. But the frustration of last night’s exit owes much to the failure of repeated lessons delivered but unheeded.

Zenit have spent serious money - they invested £77m in their playing squad this summer - and the expectation is that they will improve as this competition continues. But while Celtic allowed them to look good last night, the cheapness with which the tie was handed over ought to rankle with the Parkhead side.

Perhaps Zenit’s performance accounted for the manner of Mancini’s positivity last week in the aftermath of the opening tie. Maybe it was that he had seen enough to know Celtic had hit their peak while his own side could raise the bar significantly but few could have accounted for the Parkhead side’s ability to hoist it in their opponent’s favour so readily.