Victory has a hundred fathers. Defeat is an orphan. John F Kennedy was so right. In the days since the election, the walls of Westminster have echoed with two sounds. One is a bray. That is the noise of Tories of various stripes claiming paternity for their election success and telling everyone who will listen that they weren’t among the panickers – they were always quietly confident that clever old Dave and cunning old Lynton would get them back to power. David Cameron is honest enough to admit that he was surprised. When he lined up with Ed Miliband and Nick Clegg for the VE day ceremony at the Cenotaph, the Tory leader confided to his two victims that he thought he’d be spending the day writing a resignation statement.

The sound from Labour is a howl. Whether they be Blairite panjandrum or leftwing trade union grandee, the air thrums with Labour people saying they knew all along that Ed Miliband was a vainglorious, self-deluded dweeb who was taking them to defeat.

Labour has made one sensible choice since election day. The national executive has decided that the search for a new leader will last until the autumn. For the most part, this has been discussed in terms of the horse race. A quickie contest was assumed to favour Andy Burnham, the shadow health secretary, and Yvette Cooper, the shadow home secretary, because they start with the widest name recognition. A longer contest is thought to be of greater help to the younger, less established contenders. The more important point about a long contest is that it gives a greater opportunity to assess the candidates. Chuka Umunna came out of the stalls as the bookie’s favourite only to pull out of the race before the first hurdle. That underlines what a demanding role they are applying for and how thoroughly they must be tested before Labour makes its choice.

There was a strong case for Labour to have a complete pause before plunging into a leadership contest. Some close to Ed Miliband tried to persuade him to stay on for six months so that the party could first conduct a searching inquest into its defeat and have a proper argument about its direction. Mr Miliband couldn’t be persuaded to hang around and you can’t really blame him. Prime minister’s questions would have been torture. And who would fancy being a sort of living corpse laid out on the slab while your failures are vivisected?

As a result, Labour must now do two difficult things at once: conduct a profound postmortem and choose a new leader. There are already emerging divisions. Between left and right, younger generation and the old guard, northern and southern, those who think the imperative is to reconnect with lost working-class voters and those who emphasise the party’s inability to appeal to the middle classes. More important than any of those divides is the split between those who seek refuge from their grief in superficial explanations for this defeat and those who understand that they must think hard about the existential challenge that now confronts the party.

For those seeking false comfort in scapegoats, one obvious direction to point the finger is at the opinion pollsters and the media. I agree that the former, by wrongly telling us that the election was on a knife edge, skewed coverage of the campaign. There was insufficient attention paid to what a Tory majority government might do and a vast amount of speculation about hung parliament scenarios. This advantaged David Cameron by feeding his “competence versus chaos” theme. Campaigners of all parties agree that the spectre of a Labour minority government being the puppet of the Scottish Nationalists helped the Tories tug English voters over to them. But let’s run the counterfactual. Let’s imagine a campaign in which the pollsters had got it right and told us that the Tories were on course for a majority. How much would it have helped Labour to have known that it was more than six points behind? Would it have helped at all? Or would the party have gone into a meltdown that would have made the defeat even more calamitous?

After every campaign, there are always might-have-beens. Dwelling on them is classic displacement activity. The Tory tactic worked so well for them because it amplified pre-existing fears about Labour. When Mr Miliband declared that he wouldn’t be bullied by the SNP he just wasn’t convincing to those voters already worried that he was weak and not to be trusted with the economy.

He always trailed David Cameron when the public was asked who would make the better prime minister. That poll finding I do believe. This deficiency in the former leader will rightly make the capacity to come over as a credible candidate for Number 10 extremely important when it comes to choosing his replacement. Any candidate who says that presentation doesn’t matter should be shown the door. But simply looking for someone who might be more accomplished at eating a bacon buttie isn’t going to fully address Labour’s challenges. It doesn’t come close.

In the past week, the fallen leader has been attacked from many quarters for deluding himself that the centre of gravity had shifted and pushing policies that were too left wing for swing voters. The truth is more hideous. The individual policy items on the Miliband menu were popular. The Labour leader also had arguments that resonated when he talked about inequality. Quite a lot of Tories say so. The meta-problem was that far too few voters found the overall package believable. The swing voter in Nuneaton, Bolton and Southampton nodded along when Mr Miliband complained about the cost of living. And then they voted Tory. Even when they agreed with Labour’s diagnosis of the country’s ills, they didn’t have confidence that its prescriptions were affordable or practical.

Labour never found a good answer to the charge that it overspent when it was in government. Five years on, the contenders for the leadership are still being asked a question that should have been dealt with in 2010. Labour never closed the yawning gap when voters were asked to choose between them and the Tories on economic competence. One of Mr Miliband’s worst strategic errors was not to grasp that the voters were not going to trust him to reform capitalism until he had first convinced them that he could be trusted with the national finances and their personal livelihoods. In today’s Observer, Jon Cruddas, the party’s former policy chief, describes this moment as “arguably the greatest crisis the Labour party has faced since it was created”. That’s pungent stuff, but he has a point. When Michael Foot went down to his catastrophic defeat in the suicide note election of 1983, at least Labour had solid heartlands to fall back on. It could still rely on Scotland and northern England. Seats in the latter are now under siege from Ukip, while Scotland has returned just one Labour MP.

The traumatic defeats in the 1980s and early 90s sent a clear message about which policies Labour had to ditch and what sort of leader it needed to choose to get back into competition. As I remarked last week, the message from this election is much more complex. Labour has been annihilated in Scotland by a party running to its left. It is menaced by Ukip in northern England and the Tories have clearly signalled ambitions to try to become more competitive there. It was canny of George Osborne, who is already thinking about the 2020 election, which he hopes to contest as Tory leader, to quickly return to his “northern powerhouses”. Labour has barely any MPs in southern England outside of London and lost seats it foolishly assumed were in the bag in crucial parts of the Midlands. The election was a triple whammy for Labour that leaves it in a triple vice.

The candidates for the leadership who are not serious will be those who just pick out the bits of that message from the electorate that fit with their existing beliefs. The candidates worth listening to will be those who try to address both the scale and the many dimensions of the challenge.

It is possible to make a hopeful case for Labour. Five years is a very long time in politics. The shock defeat of 1992 was followed by a Labour landslide in 1997. The SNP will get found out eventually when Scottish voters begin to notice that its rhetoric doesn’t accord with how it actually governs in Edinburgh. Ukip will implode. The Lib Dems will take years to rebuild. The Conservatives will misunderstand the nature of their victory and take it as a licence to lurch off in directions that many voters will hate. Then the Tories will rip themselves apart over Europe.

One or more of their opponents might well foul up, but Labour would be extremely foolish to gamble on it. That was one of Ed Miliband’s strategic mistakes. He thought that because the Tories weren’t liked, it followed that the country would put him into Number 10. That turned out to be a non sequitur. His successor must not repeat that mistake.