Jonathan Agnew on England's win over Pakistan at Emirates Old Trafford

For Joe Root to say England have the belief they can win matches from almost any situation is perfectly valid.

The victory in the first Test against Pakistan, when the odds were stacked against them deep into what turned out to be the final day, is another example of why Root and his team should think that.

It was a classic day of Test cricket, with England digging just that little bit deeper to beat a Pakistan side that had been in charge, but ultimately contributed to their own downfall with some mistakes when the pressure was on.

Root, though, also acknowledged it was a far from perfect performance from England, which itself is important.

It would have been easy for him to say a win means everything is rosy in the garden, but it is actually a sign of strength of character to admit there are things England need to look at.

It is the character, togetherness and willingness to work hard that carried England to such a memorable win.

Take Chris Woakes, for example. Here is a man with a dubious record against short-pitched fast bowling, arriving at the crease just after he had seen Ollie Pope fall to a snorter from Shaheen Afridi.

Yet, there he was, a few hours later, scoring the winning runs. Woakes very rarely gets the credit he deserves, so I'm thrilled he had his day in the sun.

Funnily enough, the beginning of Saturday's play was another occasion that highlighted how under-appreciated Woakes can be.

He and Stuart Broad have been England's bowlers of the summer and Woakes dismissed Pakistan's best players, Babar Azam and Azhar Ali, the previous evening.

England still chose to partner Broad with Jofra Archer at the start of play.

Woakes is never one to complain and often seems to be the fall guy when changes are required.

However, as Saturday proved, he is an incredibly valuable asset to the England team and perhaps he has now ensured he will not again be the one who misses out.

While Woakes is someone rarely in the spotlight, his ally in England's match-winning partnership, Jos Buttler, found himself under the microscope for his wicketkeeping errors earlier in the Test.

There had been pressure on his batting, too, though we had seen signs of that slowly coming together at the end of the West Indies series.

His errors with the gloves, particularly the double reprieve of Shan Masood, who went on to make 156, are mistakes a Test keeper cannot continue to make.

Jos Buttler recorded six fielding errors in the series opener against Pakistan - the most he has recorded in a Test appearance (Opta)

Buttler himself admitted as much and vowed to keep working at it. You cannot ask more of him than that.

However, if you compare Buttler's glovework to his opposite number in this series, Mohammad Rizwan, there is a clear gulf in skill.

It leaves the selectors with an incredibly complex problem. It would be ruthless - and, if we're honest, highly unlikely - for Buttler to be left out after his contribution with the bat.

But England will know that, on another day, they will not get away with such errors behind the stumps.

It might be that, come the winter, when England are due to play Sri Lanka and India, the specialism of Ben Foakes is needed behind the stumps and Buttler has to earn his place through runs alone.

England also need to address issues around Archer and James Anderson, two pace bowlers at the opposite ends of their Test career.

Even after the win against Pakistan, Root was referring to Archer as a "90mph fast bowler", but that might be something England need to rethink.

There is no doubt Archer is capable of some electrifying spells, but more often than not his pace is in the mid-80s.

Archer is clearly very skilful, a modern bowler with all sorts of tricks, variety and slower balls. He also relies on rhythm, and often that has him at a pace we normally call fast-medium, rather than out-and-out fast.

It might be unfair to expect him to be always pushing the speed gun past 90mph. That is not to say he should not be in the team, because he has a lot to offer, but time will tell if he is the pace merchant England have been looking for.

As for Anderson, England's all-time leading wicket-taker has not quite looked himself and is clearly not happy with the way he is bowling.

Before the fourth day against Pakistan, he was on the outfield, bowling off a few paces, making sure his wrist was in the right place. That is a sign of things not being quite right.

Anderson is 38 and has repeatedly spoken of his desire to play as long as he can. That is admirable, but there also has to be the worry that eventually his body will let him down.

When you look to the winter, you wonder if England would really want to put him through Sri Lanka and India, then next summer they will be building a team for the Ashes, by which time he will be 39.

Having said all that, no one would be silly enough to write off an all-time great like James Anderson.

Jonathan Agnew was speaking to BBC Sport's Stephan Shemilt

James Anderson is finding less swing this summer than in any previous year according to Cricviz