The hostilities in Georgia are more than a war in Europe's backyard. It is a war in Europe itself, with brings potentially dire consequences.

The Georgian President, Mikheil Saakashvili, elected in a landslide in 2004 on a manifest destiny platform of restoring national unity, has miscalculated and may have stepped into a Russian trap. Vladimir Putin came to see Georgia as Russia's Cuba – an outpost of a foreign power in his backyard – and trouble has been brewing for months.

The South Ossetian capital Tskhinvali is surprisingly close to Tbilisi. But a quick campaign made no sense from Saakashvili's position of weakness. He may have built up his armed forces with American help since 2004, but his most important assets are moral, although his image as the leader of a beleaguered democracy was already tarnished by his suppression of anti-government demonstrations in Tbilisi last November.

Saakashvili may have thought the Olympics Games would give him cover, especially as Putin was in Beijing and Russia hosts the next Winter Games just over the border in Sochi in 2014. But this only made him look duplicitous, especially as he announced a ceasefire just before launching the invasion.

The Georgian may therefore already be losing the all-important propaganda war. The Russians always thought Saakashvili would be easy to provoke and have been prodding and jabbing since the spring. A minority of Nato states may argue that the conflict increases the case for Georgian membership, but in others, scepticism is more likely to grow.

A second set of lessons should be learned by Europe. It's not that European governments failed to notice the problems ahead. The Lithuanians have been agitating; Javier Solana visited Georgia in June; the Germans have been trying to broker a diplomatic solution. But EU states did not stand solid enough behind the Germans. Too many had their heads in the sand, and the wrong signals were sent to both sides. The Georgians felt isolated. We created a vacuum where Saakashvili thought he had to act on his own, and the Russians thought they could act with impunity. The lesson: even if we think an issue is peripheral, we should get involved early on, when conflict prevention is still possible.

Finally, there are some hard facts for Russia. Russian troops are on sovereign Georgian territory. There are credible reports of attacks on "Georgia proper", although the very use of the term undermines the nation's territorial integrity. It is Russia that has escalated the conflict by hitting towns such as Kutaisi, Poti and Gori, and the likely consequences will destabilise the region as a whole.

Even if Russia withdraws, Georgia will be chastened and lessons will learned by neighbouring states. The prospects for a deal between Moldova and the "Transnistrian Republic" will diminish, despite the elections due next March. Russia will feel its Black Sea fleet can stay in Ukraine's Crimea beyond the current agreed date of 2017.

If Georgia is more seriously damaged, Russia may feel it has established a veto on who joins Nato in the future. But it is not too late for the West to get properly involved. Both sides risk serious collateral damage: the Georgians to their Nato and EU ambitions, the Russians to President Medvedev's proposals for a new security treaty in Europe and to their relations with the incoming US president.

We should recognise that the Russian "peacekeepers" are not peacekeepers any more, and press for a Lebanon-style force with an international mandate that could perhaps be agreed by the nascent US-EU-Nato-OSCE mission. Both sides have miscalculated, but, for all the talk of "genocide", both have incentives to step back from the brink.

Andrew Wilson is a senior policy fellow at the European Council on Foreign Relations