An historic park in Melbourne's inner north was trashed on New Year's Eve when about 15,000 people showed up to an illegal dance party there.

An invitation to the party at Edinburgh Gardens in North Fitzroy, was circulated widely on Facebook, even though the organisers did not apply for a permit.

It featured all night DJs and amplified music in the park's rotunda.

However, Yarra City Council is blaming fellow authority the City of Melbourne for the "unprecedented" number of revellers who left behind an expensive clean up bill.