In one episode of The Simpsons the school bell rings, prompting the students to sprint for the door before the end of a history lesson. The teacher pleads with them to let him finish. "Wait a minute! " he says. "You didn't learn how World War II ended!" There's silence as the class waits expectantly. "We won!" shouts the teacher. Delighted, the class cheers, as one: "U-S-A! U-S-A! U-S-A!"

The patriotic impulse in American society is intense and pervasive. The kind of national fervour reserved elsewhere for occasional events like royal weddings, World Cup victories or major tragedies is a dormant reflex waiting for a trigger. The flags are always out; the pledge is recited every day in schools. The muscle that converts shared citizenship into a form of national genius is well-trained and prepared. By the early hours of Sunday morning, as hundreds poured into the streets to celebrate the death of Osama bin Laden, it was flexed and ready to do battle.

By lunchtime Jack Bauer, the terror-fighting star of the television series 24, was trending on Twitter. In the evening Comedy Central's leftwing dynamic duo took the baton. Jon Stewart declared: "We're back, baby," while Stephen Colbert called on al-Qaida to "suck on [his] giant American balls". The comment may have been half in jest, but the audience cheered in earnest.

While many nations suffered from al-Qaida's terrorism and few in the world will mourn Bin Laden's death, the United States is the only place where it sparked spontaneous outpourings of raucous jubilation.

The national unity that Barack Obama has sought to harness following the announcement is indeed eerily familiar. Albeit in joy rather than sorrow, it's the same kind of unity that followed 9/11. It is also the same kind of unity that rallies around flags, dismisses dissent and disdains reflection. And however comforting it may have been at the time, the consequences of that kind of unity has been disastrous.

The reason Bin Laden's death was a source of such elation is in part because almost every other American response to 9/11 is regarded as a partial or total failure. Two thirds of the people believe that the Iraq invasion was not worth it, and the country is evenly divided on the issue of whether the invasion Afghanistan is a good idea. The public mostly supports keeping Guantánamo open – but nonetheless concedes that doing so will fuel anti-American sentiment.

So the frustration of the last decade, during which the limits of America's military superiority were tested and found wanting, had their outlet in the murder of a single man at the hands of a crack team of US Navy Seals.

Having effectively declared war on the world it is hardly a surprise that Bin Laden would come to this kind of end.

This was not so much the exercise of American power as the performance of it. Coming eight years to the day after George W Bush landed on the USS Abraham Lincoln to announce "Mission accomplished" in Iraq, news of Bin Laden's death was yet another mediated milestone in this war on an abstract noun. Like the capture of Saddam Hussein, the murder of Bin Laden changes little. Al-Qaida was never a top-down organisation, and was in decline anyhow – and the principal reason for its waning fortunes is the uprisings in the Arab world, revolts that have mostly taken place against America's client states.

But to suggest that "justice has been done", as President Obama did on Sunday night, seems perverse. This was not justice, it was an extra-judicial execution. If you shoot a man twice in the head you do not find him guilty. You find him dead. This was revenge. And it was served very cold indeed.

Given the nature of the 9/11 attacks a popular desire for vengeance in the US is a perfectly understandable and legitimate emotional response. It is not, however, a foreign policy. And if vengeance is a comprehensible human emotion then empathy is no less so.

Americans have a right to grieve and remember those who died on 9/11. But they have no monopoly on memory, grief or anger. Hundreds and thousands of innocent Afghanis, Iraqis and Pakistanis have been murdered as a result of America's response to 9/11. If it's righteous vengeance they're after, Americans would not be first in line. Fortunately it is not a competition, and there is enough misery to go around.

But those who chant "We killed Bin Laden" cannot display their identification with American power so completely and then expect others to understand it as partial. The American military has done many things in this region. Killing Bin Laden is just one of them.

If "they" killed Bin Laden in Abbottabad then "they" also bombed a large number of wedding parties in Afghanistan, "they" murdered 24 Iraqi civilians in Haditha and "they" gang-raped a 14-year-old before murdering her, her six-year-old sister and their parents near Mahmudiyah. If "they" don't want to be associated with the atrocities then "they" need to find more to celebrate than an assassination. Vengeance is, in no small part, what got us here. It won't get us out.