Barack Obama has sternly warned Vladimir Putin there will be "costs" for Russia if it continues or expands its military intervention in Ukraine. But the American president did not specify what these costs might be, and this toothlessness, in a nutshell, is the dilemma now facing the US and its allies. Putin does not fear the west. On the contrary, he is once again forcefully demonstrating his deep contempt.

The idea that the US, Britain or France – the only western countries with sizeable, readily deployable, experienced combat forces – might respond militarily to Russia's invasion of Crimea cannot be taken seriously. Putin surely calculates there will be no such challenge, as he did, correctly, in Georgia in 2008, and thus moves his troops and tanks in Crimea – and possibly eastern Ukraine – with impunity. Obama, whose presidency has been dedicated to ending wars, not starting them, has shown he has no appetite for new armed confrontations, in Syria or elsewhere.

Even if Obama did want to pursue a military option, he would be hard put to make it credible. US forces in western Europe have been cut back repeatedly. The US sixth fleet, headquartered in Naples, is a considerable weapon. But to make any sort of impact in Ukraine, it would have to deploy into the Black Sea via the Dardanelles and the Bosphorus, a move that Turkey would find highly objectionable, and which Russia would regard as a direct threat.

Any decision to deploy US or Nato ground troops, if the government in Kiev asked for such help, is also hard to conceive. Given its geographical situation, in Russia's underbelly, eastern Ukraine is hardly akin to remote, undefended Mali or Chad or even Afghanistan. The Anglo-French intervention in militarily feeble Libya in 2011 involved mostly air power and was only possible with backing from US bases and aircraft carriers. Even so, it stretched British resources to the limit.

And as for Nato, which describes itself as the greatest military alliance the world has ever seen, even Obama can have no illusions about European support for a military response to Putin. Germany's Angela Merkel was feted in London last week as the powerful leader of Europe. But Germany does not do wars any more, only peacekeeping, and that reluctantly. Berlin's interest is in trade, which means keeping Russia, whose energy supplies keeps the lights on and the factories running, sweet. It is Germany, no longer Britain, that is Europe's nation of shopkeepers.

When it comes to reading Putin's mind, it seems Obama just does not get it. George W Bush famously claimed he could, saying he had gained a sense of the Russian president's soul. But that was just Texan eyewash. Putin is a child of the cold war, a former KGB agent who has said he regards the collapse of the Soviet Union as a great tragedy. For this "catastrophe" he blames the west, principally the US. Beyond the specific concerns raised in Ukraine, his number one strategic motivation is revenge for 20 years of geopolitical humiliation.

Obama said in his statement: "Any violation of Ukraine's sovereignty and territorial integrity would be deeply destabilising, which is not in the interests of Ukraine, Russia or Europe." But these are the words of a university professor thinking logically, rather than a savvy, cynical politician. For Putin, Russia's interest (and his own) would be massively served if US and European interference, as he sees it, in Ukraine is knocked back decisively.

The lesson would not be lost on Georgia (which he gave a hard smack, without consequences, in 2008), Moldova, Armenia, Belarus and any other borderland states tempted to flirt with the west. It would humble Obama. And it would be a shot in the arm for the chauvinistic, post-Soviet Russian nationalism that Putin champions.

Obama continued: "It [Russian intervention] would represent a profound interference in matters that must be determined by the Ukrainian people. It would be a clear violation of Russia's commitment to respect the independence and sovereignty and borders of Ukraine – and of international laws".

Wrong-thinking again. From Putin's perspective (one apparently shared unanimously by the Russian Duma and much of the population), the democratic deliberations of the Ukrainian people have already been tainted irretrievably by western-backed "hooligans", "terrorists" and rightwingers intent on violent insurrection. An elected president, Viktor Yanukovych, has been overthrown. The new government has no constitutional locus. Russian "compatriots" are threatened.

And as Putin sees it, the US is the last country on earth to prate about respecting territorial integrity and upholding international law. Again and again since 1991, Washington has intervened overseas in its own interests while claiming to be promoting a freedom agenda.

The Russian senator Nikolai Ryzhkov, an old Soviet-era hand, made the point at the weekend when he said Russia should be prepared for the west to "unleash their dogs on us" over Ukraine. "They ruined Yugoslavia, Egypt, Libya, Iraq, all in the name of western democracy. It's not even double standards, it's political cynicism." Viewed this way, the US and Britain do not have a moral leg to stand on.

So what can Obama do? He needs Russian help with key foreign agenda items – Iran and reducing nuclear proliferation. He needs Moscow if the Syrian war is ever to be halted. He is short of cash. And, it can be assumed, he lacks public support from a war-weary American public for any new foreign adventure.

So Putin's calculations are likely to prove right. The "costs" to Russia of its latest bit of neighbourhood vandalism may be limited to a US boycott of the next G8 summit, in June, a diplomatic freeze, or a wrangle at the UN security council, or some form of punitive trade measures or sanctions. If that sounds like a puny response, it is. It will not deter Putin, the unrepentant cold war warrior. It is just what his contemptuous soul expected.