The defending champions were outplayed on the south coast, with Pascal Gross, Charalampos Kostoulas and Chema Andrés all scoring as Brighton produced a convincing display to climb to third in the table.
Arteta felt Arsenal were second best from the beginning, with Brighton consistently winning the physical battles and disrupting the visitors' attempts to play out from the back.
"They were another gear from us in the basics of the game," Arteta said. "They were always first in the first duel, in the second actions, second balls, and they started to play from there.
"And on top of that, when we had the ball, especially in our own half, we were extremely poor technically, not respecting the game and the game principles you have to apply against a team that want to press you man to man."
The result ended Arsenal's run of eight consecutive Premier League victories and was their heaviest top-flight defeat since Brighton won 3-0 at the Emirates in May 2023.
Arteta said the problems were apparent almost immediately, claiming he could sense Arsenal were "in trouble" from the "first throw-in".
"There are a lot of moments when the ball is 50-50 and it changes hands, and most of the time it was for them," he said.
"Sometimes there were some technical errors involved that opened us up in a really difficult way, but that's something to learn."
Brighton had 24 hours less recovery time than Arsenal after their respective midweek Carabao Cup fixtures, but Arteta refused to use that as an excuse.
The Seagulls had beaten Manchester United 3-2 on Wednesday, while Arsenal overcame Ipswich 4-2 on Tuesday with a much-changed team.
"They [Brighton] knew, we knew, how tough it would be today," Arteta said. "But Brighton overcame us and had another edge that we didn't have.
"Brighton had another bite, their timing was better and when the ball was 50-50, most of the time it was for them."
Despite his frustration, Arteta said the defeat should be viewed as a lesson rather than allowing it to overshadow Arsenal's strong start.
"What we've done and the way we've competed and the amount of games we've won has been remarkable," he said.
"But this is a big lesson for all of us to understand what it takes to win at this level."