After the match, Brighton boss Fabian Hurzeler took aim at Arsenal's tactics, accusing them of wasting time while taking corners. Hurzeler later apologised to Arteta over text.
"That's all done. That's all in the past. I have huge respect for Fabian and what Brighton have done as a club," Arteta told reporters on Friday, when asked about Hurzeler's apology.
"We're going to have a really tough opponent tomorrow; we have to earn the right to win the game."
Arsenal are playing their fourth straight away game, after wins at Napoli in the Champions League, Sunderland in the Premier League and Ipswich Town in the League Cup.
Arteta said he wanted his team to show their dominance by maintaining their perfect record despite the added fatigue of consecutive away games.
"That's one of the challenges of the schedule and the team has responded so well, playing with such dominance. It doesn't really matter if we play at home or away, we want to cause the same problems to the opposition," Arteta said.
A win at Brighton will earn Arsenal a fifth straight Premier League victory and maintain their impressive start to their title defence.
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Contract extension imminent
Saturday’s game will be followed by a three-week international break, with media reports suggesting Arteta could agree a contract extension during that period.
The Spaniard, appointed in 2019, is under contract until 2027 and said he and the club remained aligned over his future.
"I think we're all very much aligned... we both have the same ambition and the same will, so whenever we have time we'll get that resolved," Arteta said.
Defenders Cristhian Mosquera, Jurrien Timber, Ben White and Piero Hincapie were due to be assessed in Arsenal’s final training session after missing the midweek win at Ipswich.
"We have another session. They are all willing to be part of it and we have another session to make sure they are fit," he added.