Bradford City boss accepts fine ahead of cup tie with Chelsea
The pair were charged for an incident during the Bantams' FA Cup third-round replay win over Millwall on 14 January.
An early foul by Lions skipper Alan Dunne triggered an on-field melee, and saw Parkinson and Parkin both sent off.
Both clubs have admitted to a charge of their players failing to conduct themselves in an orderly fashion.
The sanction for that will be decided upon at a later date.
Bradford are away to Chelsea in this weekend's FA Cup round 4.