There had been fears of burn-out – not among the athletes (with the understandable exception of Andy Murray) – but the spectators. After a summer of superlatives from the moment the Olympic torch arrived on Scottish soil to the fiery closing ceremony of the Paralympics, there had been no let-up in the cheering and clapping.

Nevertheless, concern that yesterday's biggest ever homecoming parade might be one celebration too far proved unfounded, as huge crowds converged on the city centre to greet their sporting heroes.

It seems a long time since spring, when sceptics predicted that Britain's summer of sport would be an anti-climax after the over-hyped build-up. There were doubts about cost, security and transport and fears that the organisers had oversold the product. But, despite the embarrassing Korean flag mix-up at Hampden and some ticketing problems, London 2012 was a huge success in both organisational and UK sporting terms.

The medal haul of 29 gold medals (including seven to Scots), just 16 years after winning one solitary gold at Atlanta, is a testament to the huge investment that has gone into elite sport in the interim. It also provides a potent defence of the National Lottery, which made that investment possible. It is an investment that gives everyone who buys lottery tickets a stake in Britain's (and Scotland's) success. Of course, the success of our athletes was not only about funding but also hard work. The message from Sir Chris Hoy, Katherine Grainger and the rest of them yesterday was that hard work does pay off. The challenge of the games is whether it can translate a passion for spectating into a passion for participating.

Secondly, yesterday's cheering crowd marked a sea-change in Scotland's narrative about itself, a narrative no longer limited to heroic defeat by the expectation of failure. The lesson of 2012 is that we too can be winners. That message was embodied by Andy Murray's translation from the dour to the delighted, as the Wimbledon final loser won through at both the Olympics and the US Open. If only some of that magic would rub off on Scottish football.

Thirdly, the Paralympics were more than an appendix to the main event. Supported by truly brilliant advertising, they produced a measurable shift of focus from the first to the second part of the word "disability".

Here were not only extraordinary human stories of how tragedy and misfortune can be overcome but also quite simply fantastic feats of athleticism, embodied by competitors such as 15-year old Andrew Mullen of East Renfrewshire, born with only his right leg fully formed and who just missed bronze in the pool.

The feel-good factor generated by the Olympics and Paralympics will be tested in the months to come when news of Team GB will be replaced by news of GDP. But those who dismiss our summer of sport as no more than "bread and circuses", or an expensive distraction of the country's financial woes, miss the point. In the midst of a double-dip recession and with years of austerity in prospect, everyone needs something to celebrate every now and then. Last year the royal wedding filled that brief.

It was fitting that yesterday's parade culminated in George Square before its £15 million transformation into a more suitable public space for the 21st century.

There could be no better place to begin the journey from London 2012 to Glasgow 2014. It may be a hard act to follow but we are on the road.