The greatest lie ever told about penalty shootouts is that they are a lottery. This is a recognisable and trainable footballing skill, a test not just of ball-striking and placement but research, psychology, mettle under pressure. Eberechi Eze puts the ball wide, Gabriel Magalhães sends it in the direction of the Danube: this is failure on the most brutal and unforgiving terms. But it is failure nonetheless.

The second greatest lie ever told about penalties is that fortune plays no part. Any encounter decided by 10 kicks of a football will evidently be at the disproportionate mercy of random factors: the divot, the bad contact, the goalkeeper’s guesswork (and to all the preparation that goes into the process, it remains partly guesswork). That this sport – already a sport of low scores, narrow differentials and infinite variables – chooses to decide its biggest prizes on these smallest of morsels is one of its cruellest traits.

Were Arsenal unlucky in Budapest, then? Once we sieve out the righteous rage and endless counterfactuals, the minor quibbles over major refereeing calls, Arsenal probably got what they deserved. To lose on penalties after making the defending champions sweat and fluster for 120 minutes is undoubtedly harsh. But by the same token it is hard to escape the conclusion that – through their tactics and their gameplan and their mindset – Arsenal largely brought themselves to this point.

In its purest essence, and against the best opponents, Mikel Arteta’s style of football is geared explicitly towards narrowing the range of realistic outcomes, and then catching the breaks that remain. But a strategy calibrated to earn and defend a 1-0 lead, with four centre-halves and a low block, stands or falls by those same stark measures. Fine-margins football is all very well, until you find yourself on the wrong end of fine margins.

Was any other approach remotely plausible? Probably not. Bayern Munich in the semi-final showed up the limitations of going toe-to-toe with Paris Saint-Germain on their own terms. And of course Arsenal do not possess a Michael Olise, a Harry Kane, a Luis Díaz, a philosophy based on drilled waves of lawless attack. They were missing their top two right-backs, and finished the game with a front three of Gabriel Martinelli, Noni Madueke and Viktor Gyökeres, which should at least contextualise what it was fair to expect from Arteta here.

The gulf in resources is obviously a factor, but so too the gulf in priorities. Arsenal’s recruitment in the last few windows has put a premium on bolstering the back line, adding depth, bringing up the overall level of the squad rather than signing the electrifying X-factor players who can win a big game with a moment of brilliance. Perhaps this is a strategy that met its match here. Perhaps this was a night when Bukayo Saka and Leandro Trossard, Martinelli and Madueke and Gyökeres – fine players all – were exposed just a little, handed the biggest stage in the world, and not quite filling it.

Certainly this appeared to be the subtext of Arteta’s post-match reflections, when he spoke of “needing to improve” and “find different margins”. Arteta gushed about the talent at Luis Enrique’s disposal, lamented the way they warp the gravity of the game around them, force opponents to play in their least favourite areas of the field.

And there appears to be a prevailing assumption that having finally broken their Premier League drought, with a squad approaching peak age, having pushed the best team in the world to their very last drop of sweat, Arsenal will surely take the final step before long. That this is just the start of the Arteta golden age. All of which may well come to pass. And yet it’s also worth asking: what if it isn’t? What if this is as good as it gets?

For, buried within the eulogies and paeans to this side, is a kind of paradox. We are told that this is a team who – through good coaching, a good culture and a sound process – have made the very most of the resources at their disposal, allowing them to compete with the continent’s finest megaclubs and state-owned vehicles. And yet, we are also told by many of the same people, this is also a team with ample capacity for improvement in the coming years. Think about it. Can both these things really be true at once? If Arteta has squeezed every last drop of potential out of this squad, how likely is it that there are still levels to find? What if this is a club already operating at 105% of their capacity?

The thirst for renewal is strong. New players will surely help to bridge the gap, and yet the cautionary tale of Liverpool last summer is a reminder that this process is rarely straightforward or devoid of risk. World-class players necessitate an enhanced wage structure, new tactical shades and notes, a subtly different dressing-room dynamic. A club as well run as Arsenal can count on signing more hits than misses. But the bigger the stakes, the bigger the risks.

Meanwhile, clubs who can rely on the largesse of a state have much fatter margins for error. An expensive misstep on the scale of the Neymar/Messi/Mbappé fiasco would derail most clubs for a decade. Paris, on the other hand, can simply shrug it off and go again. Manchester City can drop £59m on Omar Marmoush, £50m on Nico González, £46m on Tijjani Reijnders, £27m on James Trafford, with no real urgency for any of them to work out.

Beyond these two, many of the continent’s sleeping giants have ample room for improvement. Bayern Munich and Barcelona are clearly close. Manchester United, Chelsea, Liverpool and Real Madrid are all capable of waking from their slumber in a hurry. Future generations may marvel at Arsenal’s fortune in reaching a Champions League final by beating Bayer Leverkusen, Sporting Lisbon and Atlético Madrid. Will the circumstances really be any more favourable for them next time?

Arsenal had a strong claim to be Europe’s best team this season. And while it may be some comfort to their fans and staff that they came so close, they will also need to realise the window of opportunity at the very highest level is vanishingly small, contingent on luck as well as skill, and has no guarantees of coming again. And if that doesn’t focus minds during the long summer months, nothing will.