For a barometer of the Sisyphean challenge facing Chris Ramsey the eye had only to wander to the match-up of Richard Dunne and Sergio Agüero. To field a 35-year-old centre-back who is carrying a few pounds against the Premier League hotshot – his hat-trick here took him to 25 league goals – and arguably the world’s finest specialist finisher points to a mismatch hardly of Ramsey’s making.

The 53-year-old took over in February, after the winter window closed, and so inherited the squad that Harry Redknapp built. The XI fielded here had, with all due respect, the look of a hopeful pub team. In the 36-year-old central defender Clint Hill, striker Bobby Zamora (34), and midfielders Karl Henry and Joey Barton (both 32), plus Dunne, Ramsey was relying on a backbone that, at best, is crumbling.

Barring a minor miracle – win their final three games and see Newcastle United take no points from their last two – QPR arrived here knowing they were doomed. The question then was not if Ramsey’s side would go down but how as this might materially affect the head coach’s job prospects.

For Ramsey to enhance his chances of remaining in situ he surely required his team to resemble a gunship that continued to blaze artillery while sinking, taking casualties with them in response to the coach’s inspirational exhortations. This way Tony Fernandes, the co-chairman, might decide Ramsey could be the man to revive fortunes next year and inspire the club to bounce straight back up.

The sight of Agüero receiving a Pablo Zabaleta pass just inside the visitors’ half, taking off on a curving run that removed a host of QPR defenders and popping a finish past Robert Green inside just four minutes was the direst possible start.

It brought Ramsey to the technical area in arm-waving mode but just after the half-hour it was the Dunne-Agüero “contest” that cost QPR as City doubled their advantage, the defender fouling the Argentinian for the free-kick which Aleksandar Kolarov zipped past Robert Green from 20 yards.

To Ramsey’s credit QPR had rallied for a period between these goals, a passage that included Charlie Austin putting the ball beyond Joe Hart though he was a good yard offside.

Ramsey arrived here with a record that showed two wins and eight defeats from his 12 matches in charge and the talk was of Paul Clement, Carlo Ancelotti’s assistant at Real Madrid, and Brentford’s Mark Warburton heading up Fernandes’ list of potential replacements.

Leroy Fer, who hit the bar during the opening stages, believes Ramsey has been a positive factor. “Chris has been a good presence for us. When he stepped in I feel he made us play better. He has done a good job but we have been unlucky,” the Dutch midfielder said.

A few minutes into the second half and the camera cut to a disconsolate Ramsey. He also appeared hapless and bereft of answers as Agüero had just scored his 30th of the campaign. This time the forward profited from a Yun Suk‑young mistake to take the ball and run at Green before sending the goalkeeper the wrong way.

Fer said: “It is not over until you are down. We must try to win the game. We also have to do everything we can not to concede an early goal because if they do that, they can just play around you and score more.”

If these sentiments proved hollow and relegation was all but confirmed by the Agüero second, a look at the wider picture for QPR only makes the coming months appear bleaker. Whether or not Ramsey remains in charge there is the threat of a near £58m Financial Fair Play fine hanging over the club and, as their prime asset, Austin may well be sold.

After Agüero’s third from the penalty spot James Milner and David Silva completed the scoring and the visitors’ misery. This meant City had their best league result of the year while also leaving Ramsey’s tenure on life support.

On a day when the Brazilian midfielder Sandro was ruled out of the QPR side because of visa irregularities this only added to the sense of a club stagnating and rudderless.

Not all of it is Ramsey’s fault but he may pay the price.