"He was sad," Mikel Arteta confessed on Friday, Arsenal's beaming new head coach showing very real contrition. "The timing wasn't the best for him, but he understood."

He was speaking of Pep Guardiola, the man he also described as "incredible", "inspirational", and a guiding light in the ruthlessness of top-level management.

Arteta knew this was a hard week for his old boss. He knew it would hurt Manchester City to leave now, during a typically arduous December schedule, the champions knowing third place at Christmas was the best they could hope for regardless of the result against Leicester City.

But after Saturday's 3-1 win, Arteta can raise a glass of Yuletide spirit to his mentor knowing that, unlike the UK's railway network at this time of year, Guardiola's City are motoring along the right track.

With Leicester four points ahead of them in the table and leaders Liverpool away in sunnier climes being crowned champions of the world, defeat for City against Brendan Rodgers' side would have been a brutal blow in a difficult week. It would undoubtedly also have led to more questions about the signs of decline in 2019-20 and whether this team's relentless will to win had been further embrittled by Arteta's departure.

Those were valid concerns after 22 minutes at the Etihad Stadium. City had dominated, Riyad Mahrez giving Ben Chilwell a nightmare before Christmas as Guardiola got his attacking play entirely right by attacking entirely down the right.

Apparently, though, he didn't predict Leicester's Jamie Vardy plan. This is a striker who lives for passes over or behind the defence, playing on the shoulders of Fernandinho and Nicolas Otamendi, on a pitch where Adama Traore of Wolves and the entire Manchester United forward line caused havoc on the break, and yet City conceded from the first such attack.

Kyle Walker was dragged too far forward, Harvey Barnes' outside-of-the-boot pass was precise, and Vardy showed how even a poor touch can be devastating when you're in this kind of form, his heavy control allowing him to loft the ball over Ederson for league goal number 17 of the season.

It was an obvious tactic that still caught City cold, silencing the home crowd and perhaps leaving fans fearing their title defence all but gone before the new decade had started.

But Guardiola stuck to his guns, City persisted in their forays down the right, and it paid dividends. Mahrez skipped infield again, let fly with his left foot, and Caglar Soyuncu's obliging frame deflected the ball past Ederson.

Mahrez celebrated with gusto, his seasonal spirit apparently not reserved for his old employers. Guardiola whipped his arms up and around his head like a man drowning in eggnog, demanding more from the crowd, expecting more from his players. Mahrez then switched the play, Ricardo Pereira crumpled to the turf to trip Raheem Sterling in the box, and Ilkay Gundogan scored from the spot. "What I learned is you have to be ruthless, consistent," Arteta said of working under Guardiola. The manager's message was still loud and clear.

The second half was less engaging and certainly less worrying for City. Leicester tried and failed to release Vardy and only the excellent Jonny Evans curtailed further City inroads from Mahrez and Kevin De Bruyne. Eventually, De Bruyne left the tiring Soyuncu for dead – having driven forward, you guessed it, down the right – and teed up Gabriel Jesus for a tap-in. Ruthless, consistent. Victorious.

Guardiola does not expect to appoint a new assistant this season and time will tell how much Arteta's absence is felt, but this was a significant test for City and their ambitions this season that they passed in exemplary fashion. A sad week, but no blue Christmas.