The 13-year war in Afghanistan, in which 453 UK servicemen and women died, took the lives of more British troops than any overseas military commitment by this country in the past half century. Yet Britain’s fourth Afghan war in 180 years has been in some respects a less enduringly divisive national experience than either the Iraq war or the Falklands war a generation previously. Nevertheless the scars it leaves and the lessons it teaches must not be forgotten.

The uneasy national view of the Afghan conflict was reflected in the restrained temper of Friday’s moving but troubling service of commemoration in St Paul’s Cathedral. It is particularly well embodied in the striking contrast between Friday’s events and those after the two preceding wars. In St Paul’s in 1982, after the Falklands, Archbishop Robert Runcie preached a sermon which called for prayers for the Argentinian dead, denounced nationalism, condemned the global arms trade and characterised war as “a sign of human failure”. Less dramatically, at the St Paul’s memorial service at the end of the Iraq war in 2009, Archbishop Rowan Williams cautioned about the failure to foresee and measure the cost of the war. He also predicted – wisely in the light of the Chilcot inquiry experience – that it would be a long time before the rights and wrongs of the conflict would be resolved.

Archbishop Justin Welby’s sermon in the Afghanistan memorial service was different. It was more contained than those of his predecessors. His measured message centred on the faithfulness of the individuals who fought in Afghanistan and of the families who waited for them. Amid this honouring of faithfulness and courage, there was scarcely a note of triumphalism or national self-righteousness. But the war and its legacy remained in the background throughout the archbishop’s address.

It is not enough to feel relieved that the war is over or to draw comfort in the feeling that it could have been worse

That approach may have been helpful for the families and veterans gathered in the cathedral. It may also reflect a more general national inclination to move on. The public, like the politicians and service chiefs, seems content to put the war away in a box and not talk about it. It is a mood which combines relief that the war is over, enduring unease about the individual sacrifices – and latent scepticism about the entire wisdom, conduct and effectiveness of the conflict. It is an understandable mood. The archbishop spoke for it. But it is a misguided mood all the same.

The morning after 9/11, this newspaper recognised the need for a response but warned against an over-reaction, especially a military over-reaction. A day later, the Guardian said that pounding Afghanistan into dust “would do nothing to curb the menace of transnational terrorism”, and urged that a military assault should be an option of last resort. It risked, we said, civilian casualties, the inflaming of Muslim opinion and the danger of handing the terrorists the “holy war” they had tried so hard to provoke. The conflict could be protracted and bloody. There was a lack of clear mission aims, limits and rules of engagement.

Many twists and turns followed in the Afghan war after that. But those original warnings and concerns have overwhelmingly stood the test of time. Last year, after much effort and cash, as well as many political and military mistakes, the war ended in a western retreat, leaving Afghanistan almost as ungovernable and fragile as it was under the Taliban. Hopefully, it left the infrastructure of efficient government and the possibility of peaceful normal life in place. But this was not “mission accomplished”. It was mission ended, at best. There could be no victory parade.

It is not enough to feel relieved that the war is over or to draw comfort in the feeling that it could have been worse. There must be a public assessment of what was achieved in Afghanistan. That does not mean a second Chilcot. Nobody wants that, not least because public opposition to the Afghan war was always more conditional than in the Iraq case. But the government must commission an independent national lessons strategy, as proposed by the Commons defence select committee last year. Whitehall has prevaricated for months. The parties should put it firmly back on the agenda in their election manifestos. The Afghan war may be over. It must not be forgotten.