Unless there is some reason to use the geometry directly, I think the simplest way would be to use Select by Location using the "completely within" and "switch selection" options. Something like:
#Make Layers
arcpy.MakeFeatureLayer_management(perimeterFC, "perimeterLayer")
arcpy.MakeFeatureLayer_management(myFC, "myFCLayer")
#Perform Selection
arcpy.SelectLayerByLocation_management("myFCLayer", "COMPLETELY_WITHIN", "perimeterLayer", None, "SWITCH_SELECTION")
You could then loop through that selection (i.e. print the OID's) or export out to a new table/feature class.