It was tempting as you watched Cheikhou Kouyaté motor past Yaya Touré to stash the scene away as a concise explainer of both the 32-year-old’s decline and the issues afflicting his team. Manchester City were sluggish throughout the 2-2 draw at West Ham on Saturday and Touré, who was fortunate not to be pulled up for a foul minutes later as Kouyaté outstripped him again, was given the kind of runaround that can scar the latter stages of a decorated career.

Those lapses sandwiched a 35-yard chip to Sergio Agüero, reading the striker’s run to perfection, that resulted in a lob on to the post. Touré is sensitive to scrutiny and would probably not appreciate being made an example of here, but it happens to be his lot that no one better epitomises his team’s yin and yang. The final instalment of their January trilogy against Everton looks perfectly set up to highlight the way in which City tend to operate as two separate units: a fluid, dynamic attacking lineup operating in front of a core that too often appears laboured, disjointed and immobile.

The fate of City’s season hangs on which of these departments has the greatest influence between now and May; moving this to its logical conclusion, it is likely to be the form and fitness of Agüero that holds the key and it is difficult to think of a Premier League season whose outcome stands to be more dependent on one individual.

That extends to the Capital One Cup and Manuel Pellegrini’s selection for Wednesday’s semi-final second leg at the Etihad will tell plenty about the condition he believes his first-choice players are in for the three other fronts that lie ahead. The City manager will make changes, with Willy Caballero a confirmed starter in goal while Raheem Sterling, the returning Fernandinho and Kelechi Iheanacho – an impressive substitute in tandem with Agüero as City chased the game at West Ham – all have claims to stake.

Willy Caballero will continue as Manchester City’s Capital One Cup goalkeeper in place of Joe Hart. Photograph: Martin Rickett/PA

It is a squad who will need careful management in the coming weeks. “From tomorrow until February 27 we are going to play nine games, or 10 if we have a replay [of the FA Cup fourth round tie with Aston Villa],” Pellegrini said, with a Champions League tie with Dynamo Kyiv on the horizon that should in theory yield at least a further two outings, and while midfield numbers look strong there are doubts about the depth at either end. It would be asking a lot for Iheanacho or Wilfried Bony to hold the fort over the business end of a season if Agüero pulls up again, while Vincent Kompany’s comeback – in two weeks, according to Pellegrini – will need to be seamless if repeats of Saturday, when Martín Demichelis routinely struggled to contain Enner Valencia by fair means and Nicolas Otamendi exhibited none of the basic perceptiveness expected of a £28.5m centre-back, are to be avoided.

Keener focus will be required against Everton, whose underachievement in the league gives success in this competition added weight. In full flow, these are probably the country’s most exhilarating attacking sides so it was suitably perverse that they drew 0-0 at the Etihad in the Premier League 10 days ago; the first leg of this tie, though, was high-octane stuff and more of the same might suit a visiting team whose issues – albeit doziness replacing immobility as the chief defensive concern – broadly mirror City’s.

Roberto Martínez spent a chunk of his pre-match press conference defending John Stones, whose error in the buildup to Swansea City’s 2-1 win at Goodison Park on Sunday was characteristic of the sloppiness that has all but ended any chance of qualifying for Europe via the league route, and the chances of his doing so next season will surely lurch from slim to nil if Europa League football cannot be offered. The same applies to Romelu Lukaku, whose goal gives Everton their narrow advantage in the tie. For all Martínez’s relentless talking-up of an exceptionally talented group, the frustration that recidivism at the back has severely compromised the chances of building a long-term force with it must surely run deeper than the manager lets on; a first trophy since 1995 would at least postpone that anxiety, and when Martínez referred to this as a “momentous day” it was, on this occasion, not hyperbole.

If Pellegrini is not long for his current position, he will hope to sign off with bigger days than this. The stakes may not be as high for City but Wednesday’s tie will at least be an updated litmus test of their ability to exert control on a big occasion. The psychological damage of seeing Ross Barkley accelerate past Touré, or Lukaku bully Otamendi, would be a hefty toll to pay ahead of the February schedule if City fail; getting the job done regardless would breed the thought that, for all their lopsidedness, City are capable of negotiating their more difficult tests through sheer weight of quality. If Touré’s capitulation to Kouyaté seemed emblematic at the time, a decisive flourish from the midfielder here would make that point neatly enough.