GAA president Larry McCarthy has described some of the abuse flung at players and management as "cowardly".
He says the criticism has veered into being "overly harsh" and "unfair".
Mr McCarthy's words follow Mayo GAA's criticism of the "personal attacks" on their players and management following the All-Ireland final.
In a statement, the GAA president says words matter, and what one puts in the public domain matters.
He said the criticism emanating from many people who term themselves supporters has been overly harsh, unfair and in some cases down-right cowardly, and has gone well beyond fair analysis of team performance.
The GAA President said "critical evaluation of match performance is fine, but overly harsh scrutiny of amateur players is unjustifiable. It is inexcusable when it moves beyond the realm of what happens on the field."