The Premier League champions ended the Gunners’ perfect start to the new season, while extending their unbeaten run at Anfield to 61 games.
Having lost their last two matches to Arteta’s side, the Reds started the game brightly, unwilling to lose a third straight game.
Alexandre Lacazette was gifted the opener after an Andy Robertson error, before Sadio Mane, Andy Robertson and Diogo Jota all scored to hand Jurgen Klopp’s men all three points.
After the game, Arteta told Sky Sports that his players failed to convert their chances.
Lacazette was most culpable, as he flunked two clear cut chances in the second half, with the scores still 2-1.
Arteta said: “I felt we had chances of drawing or winning the game.
“When you come to Liverpool away, you have to score your chances and not commit the mistakes we made.
“The difference is in very fine margins. The team made mistakes in the goals and our chances didn’t go in.
“We were way more effective in other games we played against them. We gave them a good fight but we’re frustrated. We’re getting better every day.”