For those of us used to spending our journalistic time pondering the chilling strategic brilliance of News International, the past 10 days have been profoundly confusing. We have watched the leadership of the company ricochet from one crisis to the next, shutting a paper here, sacking a chief executive there, moving in and out of Parliamentary select committee range as though it were a hastily convened hokey cokey.

Rebekah Brooks's resignation on Friday was at least a week too late. It came accompanied by a frankly astonishing "mea non culpa" from Rupert Murdoch in the Wall Street Journal and an unsourced quote from Murdoch's daughter Elisabeth saying that, contrary to the impression given by her brother and father, Brooks was not a magnificent chief executive but had in fact "fucked the company".

Rupert Murdoch and his son James are often and probably erroneously credited with being scholars of The Art of War, by Sun Tzu. It is a shame the philosophical work does not carry an appendix entitled "How to handle your PR in the unlikely event of a defeat". The only aspect of the phone hacking scandal to begin to meet the scale of the wrongdoing itself has been in the clear incompetence of the company in containing and clearing up the mess afterwards. How has News Corp got it so wrong?

An unavoidable conclusion is that News Corp is short of match practice when it comes to public abasement. The arrogance of Murdoch suggesting to the Journal that News Corp handled the crisis "extremely well in every possible way" making only "minor mistakes" shows massive misjudgment, not just of the situation itself but what is needed to rectify it. What Murdoch and News Corp have proved brilliant at is assessing and squaring governments and regulators and dealing with customers. But now it has a different political problem; it has to face widespread public opprobrium, shareholder revolt and political investigation potentially on both sides of the Atlantic. It brings to mind the last disaster mismanagement, of BP's Deepwater Horizon explosion and Gulf of Mexico oil spill.

Here, the management of the company made a serious of terrible errors, starting with minimising the problem and moving on to being unable to express appropriate regret. The "live feed" of oil gushing into the sea is a strong visual metaphor for News Corporation's own polluting stream of disclosures and mishaps. One lesson that BP chief executive Tony Hayward learned the hard way is that you really do have to go and cry on the beach for the cameras – particularly in the US, where lachrymose public regret is a requirement for public wrongdoing.

James Murdoch looks unsurprisingly out of touch with public sentiment, as he has lived his life at significant distance from the populace. Even Brooks's comments of a week ago that the affair would not be over until Guardian editor Alan Rusbridger was "on his knees begging for mercy" showed how off-beam the executive thinking has become. The focus of closure should surely be about victims and practices, not about a narrow competitive revenge. The central impulse of News Corp has always been one of commercial competition; now it must think about citizens and stakeholders.

It might be convenient to blame the Guardian for persisting with evidence that the police were "too busy" to sort through, but the present problem for the company is not the source of the story but its unraveling outcome. In the US there is talk of FBI and senate inquiries into News Corp, which opens up a new front of urgent, demonstrative rehabilitation for the company. Whether this mismanagement of a crisis can be reversed remains a very open question, but not one the company can afford to get wrong.