When Britain's new Paralympic swimming star, Ellie Simmonds, said at the weekend that she "didn't want the Games to end", she spoke for many more people than just her fellow athletes. Several million of us have felt the same, buoyed for a fortnight by waves of emotion while watching the world's biggest, best Paralympics – Games that showed that the Paralympics had come of age. Even the best party has to end at some point, however, and today, as Olympic and Paralympic athletes pass through the densely packed streets of London on their farewell parade, the curtain descends on four extraordinary adrenaline-filled weeks that have done much more than provide a succession of sporting highs.

Without risk of hyperbole we can surely say that the Games, taken together, have helped this country to see itself in a new and better light, while the Paralympics have profoundly altered most people's very understanding of the term disability, the old spirit of compassion having now to contend with a newer element of respect – awe even.

The list of those most deserving thanks for a month of triumphs – triumphs rendered all the sweeter for having been unexpected – is happily long. It starts with the grand master of ceremonies, Lord Coe, and Danny Boyle, who delivered that inspirational opening – the moment, incidentally, when most of us finally breathed a sigh of relief, realising that everything was going to be all right, after all. Then there were athletes, of course, the Games' indispensable ingredient. But we should not forget a bow to the tens of thousands of volunteers whose courtesy and good cheer did so much to defuse concerns that the events might be marred by crowd crushes, traffic snarls and general confusion. Lastly, the spectators, especially at the Paralympics, merit a round of applause, too. Overwhelmingly British, as the sea of Union flags in the stands indicated, they were an open-hearted and welcoming lot – so much so that one might say they provided us with a two-week course into how to be modern British patriots. The essentials? Be proud of your own achievements but celebrate those of others with no less gusto: witness the ovation that the 80,000-strong crowd gave South Africa's "blade runner", Oscar Pistorius, when he clinched his gold in the 400 metres.

Now that the bunting is coming down, what next? How to build on that renewed feeling of national self-confidence that both Games provided, and on the success of the Paralympics in particular? Without wanting to encourage our mood of sunny self-congratulation to descend overnight into recrimination, it is important at some point to take stock, remember that disabled people generally are not that well served by this country, and to do better. There is no point in talking about the Paralympics' transformative power on the popular imagination, if, to take one example, we can't even transform the majority of our Underground stations in London to the point where disabled people can actually use them.

It is good to hear that talent scouts are busy hunting for the next Jonnie Peacock. But it would be a shame if the only legacy of the Paralympics was an upsurge of interest in the sporting potential of a highly talented and super-driven minority, rather than us seizing this opportunity to look at the position and needs of the community more generally.

There is much talk of a reawakened national identity, a renewed sense of purpose and a realisation that we are a more can-do society than we once thought. Time will show whether this is an ephemeral sensation, or the start of something new. Let's hope it is the latter, and that part of the evidence of this fresh start is a new deal for Britain's disabled.