As the champagne flowed in Manchester, the pain of defeat at Trent Bridge might have seemed long ago and far away.

But it was that pain that inspired arguably the best back-to-back performances England have put together in Test cricket since they defeated Australia in Birmingham and then Nottingham to go 3-1 up in the 2015 Ashes. It was the knowledge that England had not done themselves justice at Trent Bridge that motivated them to play some of the most consistent, tough and mature cricket they have put together since the Andrew Strauss-Andy Flower era took them to No. 1 in the world rankings in 2011.

It's worth reflecting on that Trent Bridge performance for a moment. While it was the result, in the main, of an outstanding performance from South Africa, England were also culpable for some soft, naïve cricket.

And nobody was more culpable than Joe Root or Moeen Ali. Both fell to loose - even reckless - strokes in England's first innings. And while some of their team-mates fell in more defensive fashion, they did nothing to suggest they had developed an understanding of how to pace a Test innings. With two spinners and four seamers, England looked poorly balanced and heavily over-reliant upon two or three players for the bulk of their runs.

Some of those issues remain. However, in the two Tests since Trent Bridge, Ben Stokes and Root have provided the mature performances required of the senior players they have become in this side, while Alastair Cook provided key contributions at the top of the order.

Not only did England play better at The Oval and Old Trafford, but they also played smarter, tougher, more mature cricket that showed they had learned the lessons from that Nottingham defeat, and that they possessed the hunger and commitment to complement their flair. We already knew Stokes and Root could play devastating, attacking innings. But, over the last couple of games, they have also shown they can play patient, calculated knocks that take into account the quality of the opposition and the demands of the surface. Stokes contributed 224 runs in the final two Tests and Root 180.

That is an encouraging development. While previous England teams have reacted to defeat in a variety of ways - resignation (India), denial (Pakistan) and scape-goating (West Indies and Australia) - this unit concluded that if they wanted to avoid such sensations in the future, they had to improve. So they accepted the criticism and demanded more from themselves. There is still a lot of work to do before this team can emulate the success of the Strauss-Flower era, but such honesty and desire to improve bode well.

"That's the most impressive thing," Root said after victory in Manchester. "The way we've responded to a difficult week in Nottingham has been very pleasing.

"That week wasn't much fun. It would have been very easy to sit back and sulk, but we knuckled down and worked hard and came back with a really strong response. Hopefully, that is something we can harness and learn from."

Root is the first to admit he is fortunate to inherit a team with a couple of unusually strong components. The primary constituent is that he leads a side containing two experienced and skilful seamers. The fact that James Anderson came through four Tests in succession - and finished the series with a lower bowling average, 14.10, than Moeen - is hugely encouraging for England, while Stuart Broad bowled some way better than his figures suggest. In conditions offering assistance, either off the seam or in the air, they remain highly valuable performers. "They're fabulous," Root said afterwards. "They've done it for years and hopefully they can do it for many more."

Most of all, though, he enjoys the presence of at least two outstanding allrounders in Moeen and Stokes. It is similar to two of England's better captains of recent times - Mike Brearley and Michael Vaughan - who owe their reputations, in part, to their good fortune in having fine allrounders - Ian Botham and Andrew Flintoff respectively - in their sides. In Root's case, when you add Chris Woakes to the mix - and England surely will within a few weeks - the captain is blessed with a team containing depth with both bat and ball.

"It's a great position to be in," Root smiled. "We have a few wonderful allrounders in the side.

"I said at the start of this series, it was a great opportunity for guys who had played 30-plus Tests to stand up and become senior players. Moeen has taken that on and put in some brilliant performances."

But holes remain. Most pertinently, Keaton Jennings has been unable to take his opportunity at the top of the order, while Dawid Malan has looked uncertain at No. 5 in his few opportunities to date. It is too early to come to any firm conclusions over Tom Westley (or Malan, really), but he has looked the most assured of the new batsmen in the side. With an Ashes series now just round the corner, England want far more certainty in such positions.

Perhaps that's the most encouraging aspect of this victory for England. They have defeated the No. 2-ranked Test side home and away within a couple of years and they have done it without establishing an opening partner for Alastair Cook or settling upon two other places in the top five. It suggests that, if they can fill those holes, there is considerably more to come from them as a side. It will not have gone unnoticed by the selectors that, around the county game on Monday, Haseeb Hameed, Alex Hales and Woakes were scoring runs.

"It's been hard work for the guys at the top of the order," Root said. "We have batted first on wickets that have done quite a lot. Scores of 20 or 30 have been worth double that. It has been a tough school for guys at the top of the order.

"We have three more Tests before we go to Australia and that will be an opportunity for whoever gets the chance to play. Whether that is Jennings or someone else, we will have to wait and see.

"This is the start of something. It's going to take time to develop if we want to be more consistent and make sure we keep challenging the best teams in the world; we are going to have to continue to look to improve individually and as a side. We have to harness that mentality that we've had in the back end of the series and repeat it over and over again.

"We can't just be happy with where we are."

That may turn out to be the theme of Root's captaincy. Even in the wake of a significant success, even when others might be bathing in plaudits, Root is urging his team on to more. Relaxed yet demanding; calm yet urgent; delighted though unfulfilled: this has been an assured start to Root's period as captain. If they can resolve those top-order batting issues, there's no reason he should not lead them to more success in the future.