Goals from Gabriel Jesus and Kai Havertz sealed the three points for the north London side, who underlined their first-half dominance by denying Brighton a single shot on goal.
Roberto De Zerbi's side had scored in every single Premier League game this season but had no solutions against Arteta's physical and free-flowing Arsenal.
"Incredible performance, a joy to watch from the start to the end, the way we did it against this very good team," Arteta told BBC Sport.
"Even at half time the scoreline didn't reflect that. We fully deserved to win the game. We had 15 shots (in the first half), it was a lot. We had to keep going, we don't have that accuracy in front of goal."
Brighton's best chance came at 1-0 when Pascal Gross saw his shot fly wide of the post in the 82nd minute, and Arteta said that was the unpredictable nature of the Premier League.
"You see it in every game. We had many situations to put the ball in the net and we didn't, 1-0 isn't enough," he said.
The Spaniard also had words of praise for Havertz, who has started to justify the 65 million pounds ($82.4 million) transfer fee Arsenal paid for his services, with the German netting four goals in his last seven games.
When asked if he was finally putting in the performances expected of him, Arteta said: "In terms of goals, yes.
"In terms of performances, it's exactly the same as he was at the start of the season. You can see he's confident and enjoying his football."
