George Peat, the president, and the chief executive Gordon Smith were not running the show the last time a Scotland coach’s efforts were so devoid of hope that the governing body had to bite the bullet and get rid of him. The correct decision was reached, eventually, in 2004 and Berti Vogts was dismissed. The issue then – as it is now – was timing.

When Vogts saw his side humiliated by Wales in the February of that year there were widespread calls for him to be axed immediately. The men in charge back then, president John McBeth and chief executive David Taylor, did not respond to them. Whether through misplaced loyalty, poor judgment or a dithering refusal to reach a decision, Vogts was spared.

He survived for nine more months and nine more matches after losing 4-0 in Cardiff. By sticking with him the qualifying campaign for the 2006 World Cup was torpedoed from the start. Scotland took just two points from their first three qualifiers. Only then, when supporters turned on him after a draw in Moldova, did the SFA act.

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Perceptive, shrewd football directors can judge when the writing is on the wall. Smith and Peat will know in their gut that it is over for George Burley. There is no reason to hound or abuse Burley, a decent man whose patriotism and commitment to Scotland’s cause has been beyond reproach. It was reasonable for the SFA to take a punt on him to succeed Alex McLeish 20 months ago because as a former manager of the year in the English Premier League his credentials were as good as anyone else’s. But his management has been weak and ineffective.

The nub of it is that there never has been the sense that he commanded the respect or wholehearted backing of enough of the players. That says something about them too, of course. They should have an innate pride and professionalism in their work without requiring the nannying influence of a manager they can be bothered to respond to.

He has done his best, which is more than a few of the players can say. But the fact remains that he has been unable to get his squad to perform and when things reach that stage there is no case for keeping him. Darren Fletcher, James McFadden and Kenny Miller are senior players for Scotland but none of them made any sort of imprint on Saturday’s match. The back four performed as though the basic arts of defending – positioning, anticipation, tackling – were a mystery to them.

Burley has failed in the only criterion on which a manager must truly be judged: does he get the best out of his resources? Cardiff brought the latest evidence of his inability to organise and motivate this group, not to mention the tactical paralysis which seemed to strike him as the Welsh ran in their goals.

There was never an inkling that Scotland might recover after David Edwards, Simon Church and Aaron Ramsey had gleefully capitalised on the inept attempts at defending by Burley’s back four. Three goals in 18 first-half minutes finished the match, and finished a manager too.

Alternative candidates are hardly plentiful but the SFA has to believe there are men out there who could do better even with this limited squad. Four Old Firm players and three from the English Premier League started in Cardiff. Craig Gordon was unavailable through injury but Scott Brown was the only significant absentee among the outfield men.

Their collective display was so bereft of direction and belief, as well as being riddled with individual errors and aimless passing, that they made an unexceptional Welsh side look something special. What a mercy it was that Stephen McManus and Danny Fox, the two who struggled more than anyone, were not exposed to Craig Bellamy because of the Man City striker’s injury.

Ramsey is an exciting young player, yet Scotland made the Arsenal midfielder look like a world-beater. Not coping with an 18-year-old was the latest indignity under Burley.

It was too much for dozens of supporters who left the ground when the second goal went in, in other words they had travelled all the way to Wales and been sickened within 32 minutes. Most of those who remained indulged in angry chanting and finger-jabbing towards Burley, Smith and the SFA party in general.

The game’s up when the fans turn. That was what finally persuaded McBeth and Taylor that Vogts was a busted flush and had to be replaced. The supporters have been tolerant and patient towards Burley, bordering on protective of him given how much hostile media attention he has received. Cardiff was the final straw for them.

Those who wanted Burley out at the end of the failed World Cup campaign will get their wish soon enough. No real harm was done by giving him a stay of execution. A couple more friendly defeats in Japan and Wales are blows which can be absorbed by a country which has become numb to footballing embarrassments. But there comes a time to act and Cardiff was the watershed. The SFA will not make the mistake it did in 2004 when Vogts was allowed to stagger on into the start of another qualifying campaign.

With heavy hearts, Peat and Smith will make the call now.