It could hardly have been more challenging. In fact it has felt like an impossible job at times. But the events of the last week show why Arsenal put their faith in him. "We've beaten probably the two best teams in Europe," he surmised after Saturday's FA Cup semi-final win over Manchester City.
It was achieved with the same group of players Arteta inherited from Unai Emery. There were no major arrivals in January and those they did sign, Pablo Mari and Cedric Soares, have rarely featured due to injuries. Since then, Mesut Ozil has been frozen out for failing to conform to Arteta's way of working and Matteo Guendouzi has suffered the same fate.
Instead of being weakened, however, Arsenal have become stronger.
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They remain a long way from where Arteta wants them to be, of course. A place in next season's Europa League may yet prove to be beyond them even with their wins against Liverpool and City. But what's certain is that Arteta has overseen a transformation in terms of attitude and application.
It could be seen in the way they repelled Liverpool at the Emirates Stadium on Wednesday night and it was even more apparent against City at Wembley. Pep Guardiola's side had 71 per cent of the possession over the course of the 90 minutes but it is a testament to Arsenal's newfound resilience that they only mustered a solitary shot on target.
It was fitting, too, that David Luiz was at the heart of it. The Brazilian endured a nightmarish evening when Arsenal faced City at the Etihad Stadium only a month ago, costing his side two goals before he was sent off. But Arteta stood by him and his unwavering faith has been rewarded.
This time, he was faultless, leading his younger team-mates through the most difficult periods of the game and making more than twice as many clearances (11) as the entire City team combined. Luiz is not a long-term solution in defence. There are flaws in his game which cannot be removed entirely. But Arteta has brought the best out of him exactly when he needed it.
Luiz is just one of many players to have benefited from Arteta's coaching and man management.
Shkodran Mustafi's form either side of his lapses against Tottenham has been outstanding. Granit Xhaka looks a different player from the one who lost the captaincy under Emery. Alexandre Lacazette, with three goals in his last five games, is beginning to resemble a £52m striker again.
Arteta has taken risks. Pushing aside Ozil and Guendouzi, two popular members of the squad, could easily have caused unrest. But there can be little doubt that the dressing room is behind him. He has brought a level of clarity, in terms of both communication and direction, that was desperately needed.
"You're in or you're out, you're with him or without him, and there's no discussion on that," as goalkeeper Emiliano Martinez put it in an interview with Sky Sports earlier this month.
Arteta has been clear about his "non-negotiables" right from the start of his tenure and the result is a group of players which works hard and runs further. According to tracking data, Arsenal have covered more ground than their opponents in five of their last six Premier League games.
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Hard work and determination, though, will only get you so far. What's just as important is the structure and organisation Arteta has implemented on the pitch. Defensive frailties have been hidden by a change of formation. The side is now compact and disciplined without the ball, clinical and aggressive without it.
Their pressing game has been transformed too. Emery talked a lot about turning Arsenal into a high-pressing side like Liverpool or City when he took over at the start of last season, but Arteta has actually delivered it.
It is not often that Virgil van Dijk and Allison make mistakes like the ones they made on Wednesday night. But then it is not often that an opponent lays traps for them in the way Arsenal did. It was that same commitment to applying pressure high up the pitch that caused Alex McCarthy and Tim Krul to err for the opening goals against Southampton and Norwich respectively.
Arteta has even got Arsenal playing out from the back - and doing so with the kind of conviction they lacked under the old regime. In February, there were 35 passes in the move which led to Ozil's goal against Newcastle. On Saturday, eight of the 18 passes leading to Pierre-Emerick Aubameyang's opener were played inside their own penalty box.
Arsenal now hope a season that looked beyond rescue could end on a trophy-winning high. And if Arteta can achieve that with the tools currently at his disposal, then supporters are right to be excited about what he could do if he is backed to strengthen his squad in the transfer window to come.
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