When the artist Art Spiegelman told his story of 9/11 in a graphic novel, he called it In the Shadow of No Towers. It was an arresting thought, the gloom cast not by the twin peaks of the World Trade Centre but by their absence. We have been living in that shadow for the last 10 years – but it's time we escaped it. We need to declare the end of the post-9/11 era.

Of course that will be impossible for those directly affected. No one expects – and no one would ask – those still grieving for a wife or son, a husband or sister, to put the September 11 attacks behind them just because an anniversary with a round number is looming. What deepens their tragedy is that it continues. The television documentaries, newspaper testimonies and eloquent reminiscences that have been flowing for days leave no doubt that for those directly affected, 9/11 will never let them go.

Artists and writers too will resist closing the book on September 11 any time soon. Happenings on that scale take many decades, not just one, to process. As Salman Rushdie puts it: "I think these great events have to rot down. Maybe another generation has to look at it."

But if grief and art will necessarily stay fixated, the realm of politics needs to move on. Osama bin Laden is dead; George Bush and Tony Blair are long gone from office. The two 9/11 wars, in Iraq and Afghanistan, are not over, but both now have a timetable for troops to come home. The phrase of the age – "the war on terror" – has been retired.

As for al-Qaida, it has been decapitated: as well as Bin Laden, the network's new number two and chief operational planner was killed last month, and the man branded its "foreign minister" revealed to be in Pakistani custody on Monday. Most analysts say al-Qaida is weakened, its capacity to act reduced.

Of course no wants to tempt fate with complacency. For that reason one aspect of the post-9/11 landscape will and should remain in place: vigilance. Police and intelligence agencies charged with protecting the public cannot revert to September 10 pretending that 9/11 – or, for that matter, Bali, Madrid and London – did not happen. The threat has changed, but it has not disappeared.

Other aspects of the post-9/11 order persist too. Guantánamo Bay remains open, one of the early disappointments of the Obama presidency. The US "homeland security" apparatus created a decade ago is now well dug in. Given the tenacity of such bureaucracies – plenty of cold war American military structures linger to this day – few would bet on this newer one allowing itself to be mothballed.

But it's the mindset that has to go. In those dazed days after the attacks, a new foreign policy doctrine was hastily assembled. It said that the world faced a single, overarching and paramount threat in the form of violent jihadism. Every other battle had to be subordinated to, or subsumed into, that one. And the call went beyond foreign policy. Culture, too, was to be enlisted in a clash of civilisations between Islamism and the west that would rank alongside the great 20th century struggles against communism and fascism. Christopher Hitchens confessed he felt "exhilaration" as he saw the towers fall. At last there would be war against "dull and vicious theocratic fascism. I am prepared for this war to go on for a very long time. I will never become tired of waging it, because it is a fight over essentials. And because it is so interesting."

Such talk has been a constant of the 9/11 decade but its time has passed. For one thing, it's predicated on a mistake. The right way to regard the 2001 attacks was as a heinous and wicked crime – not a declaration of war. As Eliza Manningham-Buller, the former head of MI5, argued in her first Reith lecture calling it a war "legitimises the terrorists as warriors". It's exactly what al-Qaida wanted – feeding their fantasies of grandeur – and we gave it to them.

Second, post-9/11 thinking has led to grave and lethal misjudgments. The greatest of these is agglomeration, lumping disparate and complex threats under one easy heading. The most notorious example will always be Iraq, casting that as part of the war on terror even though there was nothing to connect Saddam Hussein to Bin Laden.

But it worked in subtler ways too. The director of Chatham House, Robin Niblett – who was in Washington when flight 77 struck the Pentagon – recalls how, during the cold war, regimes in Africa, Asia or Latin America won western backing as they fought off local, domestically motivated rebels simply by casting their opponents as part of "the global Communist foe". In the past decade, the west fell for the same trick all over again. Hosni Mubarak gained a new lease on office by insisting he was holding back the Muslim Brotherhood, which he portrayed as the Egyptian branch of the global jihad. This week has brought fresh evidence that Colonel Gaddafi was playing the same game, persuading British intelligence to become complicit in his torture of dissidents, partly by painting the Libyan opposition in al-Qaida colours. "The danger of the 9/11 mindset is that you try to compress all kinds of challenges into a single threat," says Niblett.

Making the war against jihadism paramount has had other consequences too, still being felt. On post-9/11 logic, the shredding of civil liberties – condemned by Manningham-Buller as handing "victory to the terrorists" – was almost inevitable, for surely such freedoms had to take second place to the supreme threat. More serious has been the unleashing of a rampant Islamophobia – intense in Europe, recently lethal in Norway and rising in the US. That too is all but inevitable once Islamism is deemed the greatest peril faced by the human race.

Famously Tony Blair declared after 9/11 that the "kaleidoscope has been shaken. The pieces are in flux". But the kaleidoscope has been shaken again – most dramatically by this year's Arab revolutions. Whatever landscape was created once the dust of the World Trade Centre had settled in 2001 has been remade in 2011. Change has come to Egypt, Tunisia and Libya – and Bin Laden had nothing to do with it.

Again, this is not to say the dangers have receded. Would-be terrorists have seen the earth-shaking impact a spectacular attack can have – especially if it prompts a massive reaction that fuels the terrorists' cause, as the Iraq invasion did for al-Qaida. If one of the Arab revolutions fails, an al-Qaida offshoot could find purchase in that country. But vigilance is not the same as a careless, undiscriminating monomania.

Even those who were not there say the memory is so vivid, it feels like yesterday. But it was not yesterday. It was 10 years ago. We should mark the 9/11 anniversary with respect and care for those who died. But then we ought to close this sorry and bloody chapter – and bury the mentality it created.