Cosgrove clashed with New Zealand journalist Andrew Voerman at a pre-season press conference in mid-October, angrily reacting to Voerman's accusation of Cosgrove and Auckland using a loophole to allow Cosgrove to serve a two-match ban in New Zealand's National League.
The 29-year-old Englishman was banned for two matches after being sent off during Auckland FC's FIFA Intercontinental Cup loss to Saudi Arabian side Al-Ahli in August.
A competition clause that allows Auckland to field a limited number of A-League professionals in their reserves team, which participates in New Zealand's National League, meant that Cosgrove could serve his suspension in a competition he otherwise would usually not play in, making him available for Auckland's season-opening A-League game.
Voerman asked Cosgrove if he was "embarrassed" by having exploited that loophole to avoid an A-League ban, describing it as "unfair" and "devious".
A bemused and confused Cosgrove reacted angrily, suggesting that Voerman's logic meant his red card suspension could only apply to future Intercontinental Cup matches.
The Black Knights had correctly applied the powers available to them to circumvent an A-League suspension, but agreed that Cosgrove had overstepped the mark by then launching into a foul-mouthed tirade at Voerman at the conclusion of the press conference.
"Cosgrove failed to uphold the expected standards of integrity, dignity and professionalism required of a professional player," Football Australia said on Tuesday afternoon.
"Auckland FC confirmed that Cosgrove would not exercise his appeal rights and had accepted the sanction imposed by Football Australia."
The sanction also includes a fine of AU$2,000.
The one-match suspension means Cosgrove will be eligible for the October 7 derby against Wellington Phoenix.