That's at odds with recent statements from Western backers, which pointed to more open-ended and wider goals and ongoing assistance to Kyiv.
US Defence Secretary Lloyd Austin has said Washington wants "to see Russia weakened to the degree that it can't do the kinds of things that it has done in invading Ukraine". Britain's Defence Secretary Liz Truss has said Russia would have to get out of Ukraine entirely, including Crimea.
There have also been regular media updates from the US and UK on Russia's battlefield struggles and loss of equipment and troops. At the weekend US intelligence leaks boasted that the US had helped Ukraine target top Russian officers and sink Russia's flagship in the Black Sea.
Burns said Putin had underestimated the Ukrainian people's willingness to fight and said they had taken in intelligence they have received from the Americans.
On Saturday President Joe Biden authorised another US$150 million ($234 million) in military hardware for Ukraine, bringing the total package of US aid to US3.8 billion. He also asked Congress to approve more than US$33b in spending to keep things going until October.
If Putin thinks he "cannot afford to lose" then the US and other countries are providing that blowtorch of pressure with no obvious negotiated way out.
This could be the right way to approach the war: Provide Ukraine with the resources to engineer a clear defeat that means Russian forces have to withdraw. Boldness and risk-taking could be what's required here to make progress.
The quicker Ukraine can gain an advantage, the faster the economic fallout in the West could ease. A train carrying Ukrainian grain arrived in Austria as part of an effort to beat Russia's blockade of Odessa on the Black Sea. Russia is increasingly attacking Ukraine's infrastructure.
The strategy could be working. Yesterday Ukrainian officials said Russian forces had been pushed back from Kharkiv, a major city near the Russian border. The fact that Ukraine has thwarted a takeover of the country and is able to defend itself without direct Nato help is clearly preferable to official Western combat troops intervening on the ground.
Former Nato Secretary-General Anders Fogh Rasmussen said: "The mistake we made in the past was to underestimate the ambitions of Vladimir Putin, to underestimate his brutality. At the same time, we overestimated the strength of the Russian military."
However, there's an unnerving whiff of Western over-confidence about the current situation and piling humiliation onto a leader who needs to save face to survive could backfire. And how likely is it that Putin would surrender?
The old rules of a military conflict needing a political endgame still apply.