In the weeks before the Winter Olympics, Russia's critics had everything pretty much their own way. It was all shot stray dogs, double toilets and a mayor who denied that there were any gay people in his town. From there, we went straight into the sport. Different worlds, different pictures, different messages.

But there was something in between, and that something has been neglected: the image that Russia wants to project of itself. And that is unfortunate, because this image – part accurate, part delusional, part aspirational – says quite a lot about how today's Russia wants to be seen and what it aspires to be.

You can ridicule such an intention. But before you do, remember the opening ceremony of London 2012 and the ecstatic response it received. Danny Boyle's creation was hailed as achieving something no one had managed before: create a national myth for our times and tell an inclusive tale of today's Britain. Russia, which has experienced so much change in the 20 years since it emerged from the Soviet Union's collapse, needed such a national pageant at least as much as Britain did.

So it is disappointing that international coverage of the opening ceremony fixed on two things: the failure of the fifth snowflake to transform itself into an Olympic ring, and the peculiarity – as it was seen – of the Cyrillic alphabet that starts ABVG, rather than ABCD. Commentators, it seemed, could not get over Russia's nerve in having the national teams enter the stadium in this unfamiliar alphabetical order. Hungary before the Czech Republic, for instance; Zimbabwe, for once, not bringing up the rear.

But there was much more that deserved attention. Yes, there were tricks and themes that owed something to both London and Beijing. Much else, though, spoke of how Russia saw itself. Before the athletes' parade, there was something like an introduction to the Cyrillic alphabet, which was no more and no less than an attempt to devise a new, post-Soviet cultural canon.

Being a fly on the wall of the meetings that decided what each letter would stand for would have been an enlightening experience. I would love to know who was on that particular committee. The letter I was for imperiya (empire); P for Peter the Great. S, you will be relieved to know, was for Sputnik, not Stalin, one of several references to the glory days of Soviet space conquests: G for Gagarin; L for moon robot lunokhod; T for the rocket scientist, Tsiolkovsky.

Shchusev, the architect who designed Moscow's wedding-cake skyscrapers for Stalin, was also honoured, while Z stood for the Russian for combine harvester. But there was no mention of communism, or Lenin, or any other Soviet-era leader. P stood for the periodic table – a reference to the Russian scientist Mendeleev and, in effect, a renewed repudiation of the Stalin-era pseudoscience of Lysenko.

The national pageant that followed the parade showed a land of wilderness and forests, in which exotic-looking settlements grew up. The Vikings – a sore point of Soviet-era historiography – had a sail-on part, but the time allotted to the building and flourishing of St Petersburg was almost as much as that reserved for the blood, guts and 1950s-style security of the defunct Soviet Union.

Where I and, I understand, not a few Russian viewers experienced a double-take was when K stood for Kandinsky, an émigré whose art was long derided, and when Nabokov, the émigré writer of Lolita fame, was chosen for N. The letter Sh stood for Chagall.

Together, the alphabet and the pageant combined to present a Russia that was culturally inclusive, both traditional and modern, in which each age, from Muscovy through to the pluses and minuses of Soviet times, had its allotted place. Yes, some of the most painful aspects were missing – the gulag, for a start; Solzhenitsyn was rejected (too divisive?) for S – but there was an encouraging lack of dogma and militarism. You could say something similar of London 2012. But the idea – to present a Russia for today that built national pride on a continuum of cultural and scientific distinction – was largely realised.

The Sochi Olympics are at least as much about rekindling a healthy national pride for a post-Soviet Russia as they are about sport for sport's sake. The facilities, the transport arrangements and the architecturally showy buildings are designed to prove that Russia is capable of modernising – a model, if you like, to demonstrate to other parts of Russia that it can be done.

That same purpose, though, has to be conditional. Only if Sochi can maintain its shiny new identity and flourish as a world-class resort will it be any use as a model for the new Russia. If it lapses into Soviet-style decay, it will stand forever as a testament to the vanity of Vladimir Putin's dream.