Ten minutes from time as the rains came and a strangely incongruous chorus of ‘Swing Low, Sweet Chariot’ rang around Twickenham the omens seemed to be favouring Scotland at last.

These were shades of the conditions in which Scotland had twice beaten the Wallabies in recent years both at home in Edinburgh and away in Newcastle so here, at this neutral venue at a tournament that has been blessed by fine conditions throughout, it was as if the rugby Gods were favouring long be-laboured Scotland at last.

That a song despised by both sets of supporters accompanied that rain begged the question of which team that chariot was being sent to accompany this time? Perhaps, Scots dared to hope, it would be the country that produced sport’s original chariot of fire, as immortalised on celluloid, the great Scottish Olympian and rugby player Eric Liddell.

Once again, however, such notions proved fanciful as a venue that has witnessed the elimination of all three of the Home Unions to have played there hosted its most dramatic match of all at this World Cup.

Over the previous three weekends it had been the setting for some of the World Cup’s hardest fought encounters as Wales produced their comeback shock win to throw English rugby into turmoil, Australia had completed the job they started when overrunning the hosts, then those two had done battle for top spot in their pool that had the potential to make a significant difference in terms of the draw.

With Wales having put up a brave bid against South Africa the previous day, Ireland had been seen as the last standard bearers for the European game with Scotland, whitewashed at this season’s Six Nations, written off by the vast majority of their own supporters as well as the neutrals.

As Greig Laidlaw rightly claimed afterwards, this is a different Scotland team from that of six months ago and, even if there was little in the way of belief, they had offered sufficient encouragement to their kinsmen to make it worth the effort and the substantial financial outlay, to get down there and get behind them.

Rarely, if ever and certainly not in modern times since results and ticket prices have combined to make the annual trip to a ground that has so rarely been a place where Scottish supporters have experienced much to get excited about have Scotland supporters made their presence felt at the home of English rugby and if, ultimately, they were to be disappointed yet again this time, this was a very different experience for all concerned as Stuart Hogg pointed out.

“It was brilliant,” he said.

“Playing at Twickenham you’re used to getting booed and heckled all the time so to have a great support behind was incredible and we appreciate it. It was a cracking atmosphere.”

That odd moment where England’s unofficial anthem broke out, Scotland’s most committed supporters made their presence felt.

In fairness Michael Cheika, Australia’s coach, was entitled as he did, to point out, amidst all the concerns raised about the legitimate grievances raised on Scotland’s behalf if not, for the most part, by the players and management themselves, that his men had scored five tries in a World Cup quarter-final which would normally be more than sufficient to win the match.

Indeed, had Bernard Foley not endured a dreadful first half with his kicks at goal, in contrast both with how he had performed when scoring 28 points in almost single-handedly eliminating England a fortnight earlier and to the cool-headed way in which Laidlaw kept the scoreboard ticking over for his side, the margin might have been rather more telling and any controversy would have been muted.

As Scotland supporters reflect, then, on a this effort is much improved on events of earlier in the year when the team was whitewashed in its Six Nations Championship campaign, while players make bullish noises about their prospects, there are comparisons to be made with 12 years ago and a World Cup performance which saw Scotland edge out a South Seas side to reach the quarter-finals and then go on to lose to Australia in the quarter-finals.

On that occasion a margin of 33-16 was much more emphatic than yesterday’s 35-34 defeat but the over-riding impression is that after a decade and more of going backwards Scotland has got itself back to the position Jim Telfer and Ian McGeechan left it in after what was the famous duo’s final campaign together.

Once the raw emotion associated with this latest disappointment ebbs it will be an opportunity for proper, cool-headed reflection on what Scotland can achieve.

Central to that will be coming up with proper strategies that are far less reliance on imported talent such as coaches Vern Cotter, Matt Taylor and Jonny Humphreys, but more particularly back-row forwards Dave Denton, John Hardie, Blair Cowan, tighthead prop Willem Nel and wingers Sean Maitland, Tommy Seymour and Tim Visser, as renewed efforts are made to develop the sport within Scotland.

This team has failed, as was always going to be the case, to achieve their employers’ much-mocked ‘strategic target’ of winning the World Cup. Time, then, to draw a line under such fanciful thinking, understand that this is a team that has proven capable of occasional gallant performances, but could yet be successful if it can generate them consistently and, if so, identify the right strategies to build on an encouraging World Cup showing.