Chelsea struck after just two minutes through Morgan Rogers, but Arsenal responded strongly as Kai Havertz and Martin Odegaard turned the game around.
It was Arsenal's third win from three matches following victories over promoted Coventry City and Aston Villa, but Arteta viewed the performance against Chelsea as a significant step forward.
"I think it was an exceptional performance," Arteta said. "I enjoyed every minute of it from the beginning to the end, and the beginning was tough.
"I enjoyed it because the team reacted in a spectacular way. The conviction, the determination, the quality that I intend to have them constantly, it was beautiful."
Arteta believes the result was evidence that Arsenal can improve on the level they reached last season.
"It's an indication for us of how capable we are to perform at an even higher level than last season, and it depends on how we maintain and sustain that desire," he said.
Arsenal did not make major additions to their attacking options during the transfer window, with Gabriel Jesus, Gabriel Martinelli and Leandro Trossard leaving the club.
However, Havertz, Odegaard and Bukayo Saka all impressed against Chelsea, while new signing Christos Tzolis provided another threat from the wing.
Odegaard, in particular, looked closer to his best after a disrupted previous campaign.
"Odegaard has a point to prove from last season after missing so much football," Arteta said. "When that happens, Kai the same, Bukayo the same, we miss so many attacking players last season for long, long periods.
"I don't know how many times they've played together those two in the last year or so, but probably not much, and when you start to feel the chemistry they have between them and what they can produce, it's great."
Arsenal are now one of only two Premier League teams with a 100 per cent record, alongside Manchester City.
For Chelsea, the defeat brought new manager Xabi Alonso's impressive opening run to an end. His side have now conceded seven goals in three matches despite showing plenty of attacking promise.
Alonso knows Chelsea must improve defensively if they are to challenge consistently.
"We want to start having clean sheets, they will come," Alonso said. "The players are committed to working hard, to knowing that we're on the way to compete in each game.
"Not happy that we couldn't get anything, but we need to keep calm and carry on."
Arsenal now turn their attention to the Champions League, with Arteta's side travelling to Italy to face Napoli at the Stadio Diego Armando Maradona on Wednesday.