In the battle between the top flight's top two teams, it was Pep Guardiola's side who came out on top at the Emirates Stadium thanks to goals from Kevin De Bruyne, Jack Grealish and Erling Haaland.
Bukayo Saka's response for the home side from the penalty spot proved to be a mere consolation.
After leading the table for much of this season, Arsenal have now surrendered top spot, albeit with a game in hand.
Having dominated possession for large spells, defensive errors and profligacy in front of goal were key contributors to Arsenal's third league loss of the season.
"We lost it, it was an incredible battle against two teams and we had them - but we gave them the goals," Arteta, who has lost eight of nine games against Guardiola in all competitions, told Amazon Prime Video.
"We had them in big moments, but in the big moments they were better than us. We were really imprecise, we put ourselves in trouble, in certain areas of the pitch we overplayed and we got punished.
"We had three big chances but didn't put them away and that was the difference. To beat them we have to be over our level because they are such a good team.
"The atmosphere and performance was really good, if you take away the way we gave them three goals."
Arsenal are back in action away at Aston Villa on Saturday.
