Manchester United’s thrilling, physically relentless 4-2 defeat of Manchester City at Old Trafford was in many ways a typically English derby: a match full of passion, mistakes, goals, mistakes and fine attacking combinations (and mistakes).

Against that it was also in many ways an un-English affair. For a start, the most important player on either side – as United recovered from conceding the opening goal – are both available for selection by Roy Hodgson. And beyond that the pivotal figure in a match featuring the five highest-paid overseas players in the Premier league was an ambling 34-year-old, anti-glamour English midfielder who scored no goals, provided no assists, scarcely made the highlights reel, but still looked the most quietly decisive presence on the pitch.

There is no traditional English template for the role Michael Carrick has been playing in United’s revved-up midfield over the run of six impressive Premier League wins, not to mention the last nine trophy-filled years.

Carrick is not a tackler, or a hustler, or even a high-visibility metronome in the Xavi Hernández style. Instead he performs more like the footballing equivalent of a veteran head waiter: so tactful, so artfully effective you half expect to look a little more closely and notice he has spent the last 60 minutes playing in a dinner jacket.

Against City Carrick had 71 touches of the ball, more than any other midfielder or attacker. He made more passes than any other player – almost twice as many as Fernandinho – with the highest completion rate of any of the starting 22. Plus, of course, he even managed to win that decisive personal duel in the opening exchanges. Carrick’s influence is no secret: United have lost only once this season when he has started. Hence Manuel Pellegrini’s use of James Milner as a Park Ji-sung-style forward-destroyer. And for a while Milner did manage to infiltrate Carrick’s portable pocket of space, also producing a beautiful little through pass to help create City’s opening goal.

At which point Carrick flexed his shoulders and began to settle into his rhythms. There are three things United’s passing fulcrum does well on occasions such as these.

First he is an excellent interceptor, often positioning himself in exactly the right place to funnel the play into harmless areas, as he did twice in the first half as Yaya Touré rumbled forward. Second Carrick provides a place for his team to rest the ball, always available, always preternaturally calm in possession.

And crucially, in this particular performance, he can also move the ball quickly. More than simply a lateral-passing, safety-first merchant Carrick is a brave player on the ball with a veteran eye for a decisive shift of tempo. Let’s face it, he was always likely to emerge as a Louis van Gaal favourite.

Swift lateral passing between two well-grooved midfield units has been key to United’s fine results recently. Just as all four goals at Old Trafford came via swift attacks down City’s brittle left flank, the attacking plan has been based around switching the ball rapidly, often via long passes from Carrick’s part of the pitch, to create an overload of personnel out wide.

At Old Trafford, United made 87 long passes to City’s 49, with Carrick and Ander Herrera regularly passing long from midfield. No doubt there will be those who seize on this as an example of the Van Gaal “philosophy” amounting to little more than a Charles Hughes-in-a-tutu direct football hoof-athon but this is to misunderstand Van Gaal’s background.

It is only in England that the long pass is seen as quite so toxic, not so much a tactic as a non-tactic, an admission of failure. Whereas accurate, purposeful long passing has often been an important variation in the Dutch model of total football, just as many goals scored by the great Dutch teams of the 1970s featured long lateral passes, crosses from wide positions, or dashing diagonal runs.

Against City, United’s long passes were mainly diagonal, the ball ferried between two sides of a chorus: Herrera, Juan Mata and Antonio Valencia on one side; and on the other Ashley Young, Daley Blind and Marouane Fellaini, who acts a kind of human Velcro in this system, a first receiver whose job is then to shuttle the ball on quickly in search of uncovered space. The performance in defeat by Arsenal in the FA Cup last month resembled a slightly ragged early version, the long passes overdone, and too often from back to front. Here with the system working better, United brought to mind an expert hard court tennis player, moving an opponent from side to side, feeling for a weak spot, ganging up on one wing and setting City up for the big switch to that feeble wide backhand (also known as Gaël Clichy).

Van Gaal had struggled for a while with the problem of how to inject speed into his team’s attacks when his most effective players are passers not runners: of the United stating 11 at Old Trafford Blind, Fellaini, Carrick and Mata are all notably slow across the ground. And yet United still played at an unsettlingly-high tempo against City simply by releasing the ball swiftly and accurately, with Carrick the key conductor.

It is familiar modern trend, a kind of elite level quicki-taka; Joachim Löw has been known to take a stopwatch to training and urge his players to trim milliseconds off how long they hang on to the ball before passing. Perhaps the most notable part of this emerging style at United is that Van Gaal has constructed his first choice team out of various odds and leftovers, with £110m of recently signed talent on the bench on Sunday.

He has at least been bequeathed a high quality component in Carrick, a player who remains one of English football’s more understated recent grand talents. So much so it seems odder with every passing season no England manager, blessed with the midfield riches of the golden crop years, ever properly tested the idea that putting Carrick down first on the team sheet might have made the others – Steven Gerrard, Frank Lampard, Joe Cole, maybe even Paul Scholes – click into place around him.

Certainly Van Gaal, who knows a bit about team building, will be desperate for Carrick to recover from injury in time to face Chelsea at Stamford Bridge on Saturday.

It seems likely José Mourinho will have a more workable antidote to Carrick’s deep playmaking influence, not to mention an attacking system that is designed to expose opposition full-backs. Certainly it’s hard to imagine Branislav Ivanovic being as easily bullied by Fellaini as Clichy and Emre Can have been recently.

Either way Carrick’s own new one-year contract already looks a significant step towards a more concerted challenge for the title next season from this evolving, quick-passing United team whose central component remains their deep-lying brain.