An object was also thrown onto the pitch during the World Cup qualifier against Qatar.
Fifa, football's governing body, previously warned the HKFA over booing.
The anthem has been shared by Hong Kong and mainland China since the former returned to Beijing's control in 1997.
But anti-Beijing feeling has increased in Hong Kong in the wake of large protests last year against central government plans to impose candidate lists for elections in the territory.
Mr Brian Leung, the Chairman of HKFA, said: "We will promote the message of 'not booing' on all our media channels and will not punish the fans who threw the object onto the pitch as we don't know who did it."
A statement by the HKFA said Fifa had warned it that "any further infringements will lead to more severe sanctions", asking fans to "refrain from such action at all future matches" to avoid additional punishment.
The association previously said that it would be "disappointed" if Fifa punished them for the booing on 8 September, which it later blamed on "a small minority of fans".
Hong Kong's next international match is against Myanmar (also known as Burma) on 7 November, followed by a home game against mainland China on 17 November - likely to be of particular concern to organisers given the tensions involved.