Peterborough have admitted failing to control their players and staff during the melee after the home defeat to Notts County last month.
Both sides were charged by the Football Association following the mass confrontation and Posh are now waiting to hear of their punishment.
A club statement said: "Peterborough United would like to apologise to all supporters who may have been upset or affected by the melee following the final whistle."
The statement added: "It is never the intention of the football club to be involved in incidents of this nature and the club is taking strict internal measures to ensure that such events are not repeated."
Head of sports science Ben Mackenzie - who was handed an individual charge of violent conduct - has requested a personal hearing.
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