The Arsenal manager responded sharply after Hurzeler accused the league leaders of "making their own rules" during a tense match on the south coast. Arteta refused to apologise for his team's approach, insisting the focus was on winning in the crucial final stretch of the season.
Bukayo Saka's ninth-minute effort proved decisive. The winger cut inside and fired a shot from the edge of the area that deflected off Carlos Baleba and slipped through the legs of Brighton goalkeeper Bart Verbruggen.
The narrow victory was Arsenal's third successive league win and moved them seven points clear at the top of the table after Manchester City were held to a 2–2 draw by Nottingham Forest.
After the match, Hurzeler criticised Arsenal's game management, pointing to several moments when goalkeeper David Raya went down for treatment and delays at set pieces.
"I think there was only one team that tried to play football today," Hurzeler said. "Have you ever seen a goalkeeper go down that many times in a game? They make their own rules."
Arteta, however, was unmoved by the comments.
"What a surprise," he said when told about the criticism. "If you look back through previous games you will always find comments like this."
The Arsenal boss praised his squad for their resilience in a difficult away match.
"I love my players and I love the way we compete," Arteta added. "When you are in the position we are in, the opposition will try to take that away from you. That is normal. That is sport."
Arsenal were far from fluent, with Brighton creating several chances after the break, but Arteta's side defended resolutely to secure another crucial three points.
With eight league games remaining and momentum firmly on their side, Arsenal's pragmatic approach could yet deliver the club's first English league title since 2004.