Eight years ago, Mr Barack Obama ascended to the United States presidency on a surge of optimism. From the grim depths of the War on Terror and the Global Financial Crisis, his slogan "Yes, we can!" expressed rebounding confidence. America could rebuild its economy, its social fabric, its political institutions and its place in the world. His leadership, it seemed, would make all the difference.

It is hard now to recapture that sense of promise and opportunity. Mr Donald Trump's election as Mr Obama's successor shows all too plainly how far Americans' hopes at home have been disappointed since 2008. And a glance around the world today reveals how far the reality in foreign policy has fallen short of the prospect Mr Obama seemed to offer just eight years ago.

Back then it seemed that America could withdraw from Iraq quickly and cleanly, leaving a country that was stable, prosperous and pro-American. It seemed that a sustained effort in Afghanistan could create a modern, effective state able permanently to resist the Taleban. It seemed that Mr Obama's charisma and American ideals channelled through Twitter and Facebook could transform Arab politics, reconcile America to the Arab world, and create the basis for renewed US regional leadership.

Back then it seemed that a simple diplomatic "reset" could restore relations with Moscow and turn Russia into a willing supporter of America's global leadership. And it seemed that Mr Obama's inclusive brand of international statesmanship could likewise persuade the North Koreans to abandon their nuclear weapons and Chinese to put aside their growing power and shelve their strategic ambitions in Asia in favour of remaining a "responsible stakeholder" in the US-led regional and global order.

Perhaps most tellingly, back then it seemed possible that America would lead the world in abolishing nuclear weapons. Mr Obama's Prague speech conjured a world in which America no longer needed nuclear weapons because it no longer had any serious rivals for global leadership, and its conventional forces were anyway so overwhelmingly powerful that nuclear forces would be unnecessary to meet any challenge.

Compare all this with the world we see today. Iraq's failure and the toxic legacy of the Arab Spring have contributed to the disastrous collapse of key states across the Middle East, with appalling humanitarian costs today and profound long-term strategic consequences on a scale we can as yet hardly comprehend. In the process, a new and even more virulent and violent strain of anti-Western extremism has been unleashed, and Iran's influence throughout the region has grown.

In Afghanistan, the Taleban has returned as the US-led intervention has wound down. The fragile social, political and economic foundations of an effective state are crumbling, and it is increasingly plain that the immense effort and sacrifice of America and its allies over a decade will prove a sad and costly failure.

Russia, far from being reconciled to taking its place in a US-led world, has emerged as a serious strategic rival. It has mounted a sustained and effective campaign to rebuild and extend its own spheres of influence on its Western borders and in the Middle East, promoting visions of international order directly at odds with Washington's and starkly undermining US claims to regional and global leadership.

In Asia, North Korea has not relinquished its nuclear weapons, but instead moved swiftly towards a fully operational nuclear force and now seems to be building the capacity to target the US itself.

And finally, of course, there is China. Mr Obama's early hopes that Beijing could be charmed into accepting America's vision of the Asian regional order did not survive his first bruising encounters with the Chinese leadership in 2009. His subsequent "Pivot to Asia" was supposed to toughen the message to Beijing, but it proved so halfhearted as to be counter- productive.

Instead of showing Washington's resolve to resist China's challenge and defend its leading position in Asia, Mr Obama's feeble responses to Chinese initiatives and provocations have only underscored how swiftly the distribution of power and influence is shifting China's way.

Overall, it is a sad record of disappointed hopes and declining influence. Naturally one asks who or what is to blame. Many people say it is Mr Obama himself, because he has been too cautious in using America's power. They argue that a bolder president could have avoided all these disappointments and reasserted US global leadership.

But is that really so? Were there really opportunities to exercise US power that Mr Obama missed? The closer one looks, the less clear it becomes what these missed opportunities were. No one can credibly explain want precisely the President could have done to stem Syria's slide into chaos, or steer Egypt's popular revolution towards a genuine democracy.

There is no clear evidence that a longer and deeper commitment in Afghanistan would really have succeeded where the immense effort already made had failed. There were no credible military or diplomatic actions that could have been taken to do more than was already done to contain Russia's intrusions into Ukraine or Syria. And there was no obvious way to resist China's assertive behaviour in the South China Sea without risking a catastrophic conflict.

The problem, then, goes much deeper than Mr Obama and his policies. It stems from a basic mismatch between America's bold objectives and its limited means. It still seeks to assert its leadership globally and reshape regional affairs around the world, just as it did back in the days before 9/11, when people spoke of America as the sole unipolar world power.

That was never really true, and the evidence of the past eight years shows that it is certainly not true now. America might still be the world's strongest state, but it faces formidable opponents in many of the world's key regions, and it cannot deal with all of them at once, or even any of them singly, without an immense and costly effort.

At times this most thoughtful of presidents showed that he understood this basic mismatch between his country's objectives and its resources, and that is why he was so cautious about committing America to interventions where the costs were high and the outcomes uncertain. He deserves credit for that.

But he never really set out to explain this to the American people. In his major set-piece speeches, he still reassured them that their country had all the power it needed to lead the world, even when his actions showed clearly that he knew how far this was from being true. Not "Yes, we can" but "No, we can't".

So Mr Obama's failing in foreign policy was not that he did not do more, but that he did not explain to Americans plainly enough why he, and they, could not do more. That task he leaves to his much less thoughtful and much less eloquent successor.

•The writer is a professor of strategic studies at the Australian National University in Canberra.