To be fair to Raheem Sterling he did get one thing right this week. The build-up to this match had been dominated by that self-promotional video, during which Sterling declared himself “flattered” by talk of a £50m move to Arsenal. On this evidence he’s got a pretty good point, too.

Football has a grand inglorious tradition of ill-advised pre-match pronouncements. Quite where Raheem Sterling: Knowing Me Knowing You (special feature: Raheem’s Big Pocket) stands in the pantheon of self-defeating self-aggrandisements remains to be seen. Perhaps in the ongoing power play over contracts and transfers it will eventually be judged a triumph. But on a cold, dull April afternoon at the Emirates the ballad of Raheem Sterling took a chastening even slightly poignant turn.

Having spent the week destabilising the club he will now perhaps claim it is his right to leave in search of one that “matches his ambition”. Sterling flickered on the fringes here before winning a consolation penalty in a 4-1 defeat that has, if not killed off then mortally wounded Liverpool’s chances of making the Champions League next season.

For Sterling there was also something telling in the details of a match decided by eight minutes of high-grade attacking incision led by two players Arsenal have splurged heavily on in the last two years. Mesut Özil and Alexis Sánchez both cost less than Sterling’s proposed £50m price tag. Both are proven heavyweights of European club football. Both were stars of the World Cup. And both are, for now anyway, in a different league to a player who has in 14 months of regular first-team football seen his achievements – not his talent, which is undoubted – puffed out of all proportion by Premier League bombast and the lucrative modern burden of playing for England.

Liverpool had played well enough in the opening 37 goalless minutes of this match. For their manager this was another Funky Brendan Saturday as the visitors emerged in a fluid, alternating shape that was something between a 4-3-2-1 and a 3-2-3-1-1, with Sterling the constant in a lone striker’s role. It is a familiar approach away from home, where Sterling has been impressively spiky shielding and chasing the ball, as he was here early on, fending off Per Mertesacker with a flex of that muscular rump.

With 20 minutes gone Sterling really should have opened the scoring, although the fact he did not was hardly his fault. Philippe Coutinho’s lovely little pass through the centre put Lazar Markovic in on goal. Inexplicably Markovic passed to his left rather than shoot – and passed horribly too. Sterling, wrong-footed, saw the ball bobble past him with the goal gaping.

After which came those decisive eight minutes. Özil was at the heart of it. His pass out to Aaron Ramsey on the right was superbly timed. From there Héctor Bellerín grooved into the box and caressed a lovely finish into the far corner. Moments later Özil was hacked down by Mamadou Sakho just outside the area. He sprang back up to his feet, placed the ball and curled a delightful free kick into the same spot.

Finally, just before half time there was another pointed clearing of the throat for Arsenal’s existing attacking midfield as Sánchez scored a sublime third, hurdling a challenge after some fine interplay between Ramsey and Olivier Giroud (who would later score a fourth) and spanking a dipping shot past Simon Mignolet. Dear Mr Sterling. Thank you for your interest in the role of attacking midfielder. Please be assured we will keep your details on file should a similar position arise in the future.

This is, of course, a little harsh. Sterling is a fine emerging player who looks set for a stellar career if he can continue to progress from here. But the fact is the farrago over his new contract simply exposes the hall-of-mirrors distortions, the basic cash-driven excitability of English football. Sterling remains, for all the fine moments, a work in progress, a player whose control and lateral movement can be breathtaking, but who has still scored just once for England and nine times in the Premier League for Liverpool in his breakout year. By contrast Sánchez, a marker in Sterling’s position, has now had a hand in 31 goals for Arsenal in all competitions (20 goals, 11 assists) so far in his debut season.

Özil also thrummed up effortlessly though the gears here, passing brilliantly, and showing the extra strength in possession of his newly bulked up physique. Since his return from injury Özil has three goals and four assists in eight matches. It seems pretty clear Arsenal are little more than a stalking horse in the wrangle over Sterling’s immediate future (Manchester City the only really obvious destination). But the obvious question by the end here was where exactly this hypothetical £50m recruit might hope to get in the starting XI. Arsenal have their weaknesses, but an absence of scampering inside forwards isn’t one of them.

Whereas Sterling simply looked like what he is: a hugely promising 20-year-old who has yet to explore the outer fringes of his talents Arsenal have now won 10 of their last 11 Premier League games and will surely be in the Champions League next season. Depending on his movements from here, Sterling perhaps has a better shot at joining them one way or another than the rest of his team-mates – although this was an afternoon when his prospects on both fronts were hardly advanced.