What a failure this was for a manager as martinet-like as Rafael Benítez. Chelsea's performance was a technocrat's worst nightmare: a malfunctioning muddle. But do not blame it on the bogeyman. At least not all of it: Benítez is not the chief cause of Chelsea's problems because many of them pre-date his arrival. But nor does he appear to have the solution to them.

Chelsea were European champions when Benítez took charge in November but they were also a creeping mess and already flunking out of the Champions League. So much for mitigation; to his discredit, the Spaniard has not brought order so far and this defeat leaves Chelsea at serious risk of slipping out of the top four. There is a greater likelihood of Tottenham and Arsenal leapfrogging their London rivals in the table than of Chelsea overtaking either of the Manchester clubs. Chelsea are in real jeopardy of surrendering the opportunity to atone in next season's Champions League.

Benítez has played a poor hand poorly. And yet he started his reign promisingly, signalling straight away that he had identified a major imbalance in the squad that his predecessor, Roberto Di Matteo, had been unable to rectify. Benítez's instant innovation was to shift the centre-back David Luiz into midfield to fill the destabilising void there. The Brazilian duly connected two parts of the team – defence and attack – that had frequently, since the loss of the likes of Michael Essien and Michael Ballack, seemed condemned to toil in isolation, reliant on flashes of individual inspiration to compensate for systemic failure.

It soon transpired, however, that Benítez's normally iron-coated convictions were skimpily clad – for he did not persist with David Luiz in midfield and quickly redeployed him at the back, though again the inadequacies of Chelsea's squad made the manager's travails understandable, what with John Terry's knee injury and the lack of anyone on a par with Branislav Ivanovic at right-back.

Terry was available again at the Etihad but Benítez suggested the 32-year-old was not "fresh" enough to start after his exertions against Sparta Prague in the Europa League on Thursday, which raises the questions as to why Terry had played in that match. His omission against City was costly not so much because his team missed him in defence but rather because they missed David Luiz in midfield, where Mikel Jon Obi and Frank Lampard were overrun by Jack Rodwell, Javi García and Yaya Touré.

This was Rodwell's first start for City since September and at times it was tempting to declare it the match where he came of age and proved that Lampard is past it. But just as the ridiculing of Chelsea's decision not to award Lampard a new contract has been excessively disingenuous, so too would it be unfair to declare the 35-year-old worthless.

The problem here was that he was played out of position: he can still have residual value as an advanced midfielder but does not have the presence to play at the base of a 4-2-3-1, as he was supposed to do here.

Lampard was easily bypassed, as was Mikel. Benítez had hoped that after returning from victory in the Africa Cup of Nations, the Nigerian would give sustenance to the argument that he is an unsung workhorse during his club's golden era; instead his displays have strengthened the widespread belief that since arriving seven years ago he has been a lucky piggy-backer on the club's success.

Certainly it seems likely that Oriol Romeu would have featured more if he were not injured and, while much has been made of the oddness of Chelsea's decision to leave Romelu Lukaku on loan at West Bromwich Albion, the midfield shortcomings make letting Nathaniel Chalobah go on a gap year to Watford look equally unwise. Chelsea's central midfielders were so flimsy that Roberto Mancini decided early in the second half that the home team could retain their superiority there even if he withdrew Rodwell and introduced another striker, Carlos Tevez.

The Italian was proved right, notably for the opening goal, when Yaya Touré exposed the presence of Mikel and Lampard as pitiful tokenism when he sidestepped them at the edge of the area and curled an exquisite shot beyond Petr Cech.

Benítez was right to replace Lampard, who of course had also missed a penalty by the time he was substituted, and the manager briefly deployed Ramires in the middle. The Brazilian is better further forward but he is at least more dynamic than Mikel and Lampard. Benítez, however, tinkered again and, when Mikel was taken off, Ramires was shunted to his third position of the day, at right-back. Sergio Agüero exploited his discomfort there to tee up the second goal, leaving Ramires floundering in his wake as he darted in off the wing to set up Tevez.