For Arsenal, who were made to seem no more than a mild irritation at times by a brilliantly well-grooved Bayern Munich, it could have been much worse. In the end Arsène Wenger and his team will take, if not hope, then at least a spritz of salvaged dignity to the Allianz Arena after a decisive-looking, 3-1 first-leg defeat. For Wenger, by turns excitable, downcast and rueful on the touchline there was at least the spectacle of this diminished and transitional Arsenal team belatedly rousing themselves; but in the end they were simply short of the required quality against a composed and unremittingly focused Bayern. The Bavarians will take some stopping in this competition – just not, as it turns out, by Arsenal.

It was unfortunate but still perhaps instructive that the visit of these – other-worldly, if we are to believe the pre-match hype – opponents coincided with Wenger's most troubled week in England. Depending on whom you choose to listen to, Arsenal's manager arrived here in a state of imminent personal meltdown or, in his own words, ready to embrace "a fantastic opportunity" to win the Champions League. For all the recent black eyes and the sense of a team with too many pale imitations of what was once the real deal – a Thierry Henry-lite here, an own brand Cesc Fàbregas there – the truth is, as ever, somewhere in between.

Those who came here expecting a public outpouring of anguish from the home crowd were always likely to be disappointed. Outclassed Arsenal may have been but their support, rueful rather than full-throated, stayed with them.

As the match kicked off in the thrillingly cinematic fug of the Bayern flares Wenger had looked almost puppyishly animated on the touchline, dressed in back-to-basics, light grey business suit, the familiar sagging, quilted gown briefly left on the peg. In the circumstances Bayern's opening goal after seven minutes, beautifully finished by Toni Kroos, felt like a chop across the windpipe. Wenger drooped visibly at the prospect of a horribly instructive 173 minutes of football against a team who already looked not just technically but physically intimidating.

At times the opening 20 minutes were almost cruel as the visitors preyed on Arsenal's weakened left side: Thomas Müller and Philipp Lahm, a match for anything in club football, were confronted here by Lukas Podolski's part-time tracking back and the redeployed Thomas Vermaelen. It was no surprise that Müller's second goal came from that side. With 20 minutes gone the Bayern fans were already singing "Football's coming home", the sense of epic-scale entitlement exuded by this modern footballing juggernaut tangible at times.

Before kick-off there was a tendency to linger a little too sensuously on the many chastening triumphs of the Bayern system, the premium-badged, corporate-familial coherence, the high-spec academy assembly line – the implication being that Bayern represent the über-engineered executive poke-mobile on which Arsenal's puttering hybrid is based. It is, of course, a far from robust comparison given Bayern's status as a genuine regional powerhouse. But there was a palpable sense of maturity about the visitors, a strut that is entirely merited.

Could Arsenal have played another way, perhaps refusing to come out and leave the gaps that were so ruthlessly exposed? Beyond the frustration at Arsenal's player-shedding programme there is discontent too with Wenger's fixed-wheel tactical plan, an approach exposed by the decline in quality of player available. Some part of the pre-match doom was related to his insistence on staying true to his principles of lightweight passing football, where another manager might have the instinct to spoil successfully against superior opponents.

There were some tweaks to the starting lineup. Theo Walcott foraged gamely at times as a central attacker and, as Arsenal were driven forwards by Jack Wilshere, who looked in a different league from his team-mates, Walcott leapt with endearing optimism in the general direction of a succession of crosses that Olivier Giroud might have relished. Otherwise it was a game but callow Arsenal, pressing the black shirts as they retained possession but at the same time leaving alarming spaces behind for the strolling Kroos to pick out from his central position.

And by half-time the tie was pretty much dead, in part because of Bayern's two away goals but more because of the clear sense of a team operating at a level above, exposing the wider problem of an Arsenal squad that now houses too many players of middling quality, centre-backs who mark slackly, a midfield that was often made to look eager but lightweight. Arsenal did come out energised after half-time, pressing higher up the pitch and with Wilshere (whom Arsenal could do with four more of) inventive to the end. Podolski's equaliser came from a corner that Manuel Neuer flailed at. Mario Mandzukic's late third goal gave the scoreline the weight it deserved.

For Wenger eight seasons without a trophy – running concurrently with European football's extant Billionaire Years – now look a certainty. Afterwards he seemed gently resigned in his praise of "an excellent opponent".

Jupp Heynckes had just been asked if this was the end of Arsenal as a European force. That he simply batted the question away said much about Bayern's sense of self-possession, plus also a little more about the ongoing travails facing Arsenal's manager.