Ake strike lays down Man City marker on Arsenal
The sides will meet twice more in the next three months in the Premier League with the title on the line.
Arsenal lead City by five points at the top of the table and Arteta believes the Gunners have to put the defending English champions to the sword when they have the chance.
The Arsenal boss showed a first league title in 19 years is his priority by making six changes with Martin Odegaard and Gabriel Martinelli among those left on the bench.
But the visitors still had chances early on as Takehiro Tomiyasu and Leandro Trossard on his full debut forced Stefan Ortega into flying saves.
"Really disappointed. I think we could have got much more out of the game," said Arteta.
"We had big situations in the game and we didn't put them away. In the big moments, in big matches you have the make the difference. That is how you win these games."
City were also far from their free-flowing best with Erling Haaland often manhandled by Rob Holding before the break.
The Norwegian saw an ambitious overhead kick from long range cleared by Tomiyasu with Arsenal goalkeeper Matt Turner stranded before Kevin De Bruyne curled City's best effort of the first half inches wide.
Guardiola had made just one outfield change from City's 3-0 win over Wolves.
However, it was his one of his substitutes, Julian Alvarez, that brought a lacklustre second half to life 26 minutes from time.
The Argentine's long-range effort cannoned back off the post and from the rebound Jack Grealish's pass picked out Ake, who curled into the far corner.
"It was the first one I ever scored with my right foot so pleased with that," said Ake.
Arteta responded by throwing on Martinelli, Odegaard and Oleksandr Zinchenko.
The visitors nearly hit back immediately as only a brilliant clearance from Aymeric Laporte denied Eddie Nketiah a tap in.
But Arsenal failed to create another chance to equalise as City laid down a marker on the challengers to their crown as the dominant force in English football.
"A tight game against a really difficult opponent and we won it," said Guardiola, who had billed the clash as a barometer of whether his side could reel in Arsenal in the title race.
The sides meet again at the Emirates on February 15 before a rematch at the Etihad on April 26.