For two managers new to English football, bringing their own ideas and cultures to these shores, it did not take long to experience the full chaos of the Premier League in all of its maddening, unpredictable, helter-skelter glory. At half-time, as Maurizio Sarri and Unai Emery went back to their dressing rooms to digest a splurge of goals, misses and some harrowing defending, it must have been a challenge to know where to start to try to make sense of it all. The lurching turbulence and shifting tension was relentless. Sarri did not mind admitting that during the most wayward period for his team he would have been better off smoking than watching.

At one point he scribbled notes furiously – actually, during some of the quieter, more straightforward moments. Later on it was evident that anyone’s notes should have resembled a Jackson Pollock.

Sarri has abundant qualities to bring something fresh to Chelsea and Emery is trying to change the energy at Arsenal; if the merry wildness of this encounter taught them anything about their task and their players it is that a sensible evolution does not come easily. Not when it is possible to have three completely different matches within 90 minutes.

First came the Chelsea exhibition, then the Arsenal surge, and finally a more even joust that was decided when a charged-up Eden Hazard cantered on to the pitch with armour glinting heroically and a magic wand for a lance. The extent of his impact was unmistakable – Sarri witnessed how his team have one personality without Hazard and a far richer one with him. No Hazard, no celebration for Marcos Alonso’s match-winner.

Arsenal’s players react in frustration after their comeback was thwarted by Marcos Alonso’s late winner. Photograph: Daniel Leal-Olivas/AFP/Getty Images

The Italian has the good fortune to be trying to find his way with wins on his side. No such luck for Emery, who must feel aggrieved to find his team stuck on zero points. He carries the unfortunate distinction of becoming the first Arsenal manager to open a season with two straight losses since the very first season of the Premier League rebrand in 1992-93. That was always a strong possibility given the challenging fixtures, but what must rankle is that Arsenal gave themselves an opportunity to seize against Chelsea. The first game against Manchester City was always likely to be too hard a lesson, but here his team delivered moments of genuine promise before falling to the late sucker punch.

Fall they did. It was a sign of the effort they put in that some of the players slumped to the turf at the end. Petr Cech went over to Héctor Bellerín, who had trundled up and down the right flank with so much enthusiasm, to empathise as he stretched out the full-back’s aching hamstrings.

Emery’s own response in this situation is to ask for calm. Perhaps these are points that would have been lost in any case had these fixtures cropped up at different parts of the season. The most important thing is not any public overreaction, but the temperature within his squad. He has to encourage his team to take what positives they can as they endeavour to restart next Saturday against West Ham.

Sarri is under no illusions that Chelsea have to sharpen up the defensive aspect, and he wants his team to press more effectively from the front. For any new manager trying to make his own imprint on a new team in a new league having a trusted ally on the pitch, a player with whom your gameplan is connected, is a blessing. Chelsea began with a flair and fluency that impressed and the influence of Jorginho, Sarri’s old charge from Napoli, was telling. The Italo-Brazilian’s alertness and intelligence in opening up play was a feature that gave Chelsea an early leg-up from Pedro.

Chelsea looked super-relaxed given how their opponents were so easily unpicked in the first 20 minutes, and when Shkodran Mustafi was exposed in a one-on-one Álvaro Morata doled out the punishment.

Arsenal’s own chaos theory was exemplified by their two-phase reaction. At first their sense of shellshock was enhanced as, despite a generally abject spell, they managed to squander two outstanding chances. Pierre-Emerick Aubameyang looked chastened to shoot over the crossbar. Henrikh Mkhitaryan scratched his head as if he had an itch that was like a form of madness after ballooning into the stand.

As it turned out, from this double disappointment of playing poorly and wasting the chances to come back, Arsenal reacted with great spirit. Their two-goal riposte owed much to players whose character was tested last season when they were scapegoated during difficult away days in the energised Bellerín and enterprising Alex Iwobi, as well as Mkhitaryan. Emery is learning about his players for better or not so good, and his capacity to take off Granit Xhaka and Mesut Özil shows his readiness in all the chaos to give all his players a chance.