On Friday night, there were violent scenes in the Sandy Row area of Belfast as well as in Londonderry on Friday.
Questioning why PSNI officers must always "face the brunt of this pointless violence", the Federation went on to say: 'Destroying your own communities is not the way to protest or vent'.
"What I would ask is that people with influence, people in local communities, would dissuade young people, or anyone else, intent on causing violence or intent on harming police officers".
Police in Northern Ireland have appealed for calm after officers were attacked with petrol bombs and cars were set on fire during a second night of unrest.
Police said it was the fifth consecutive night of disorder in Derry on Friday, when 12 officers were injured by a large group throwing masonry, bottles, petrol bombs and fireworks.
Three teenagers, aged 17, 14 and 13, are due to appear at Belfast Youth Court on the same date.
Police have appealed to motorists to avoid the Cloughfern Roundabout area of Newtownabbey.
Four adults - three men, aged 25, 21 and 18 years old, and a woman, aged 19 - will appear at Belfast Magistrates' Court on 30 April.
"I think it's a tragedy that any child in Northern Ireland is sitting in a custody suite this morning and facing criminal investigation, possibility of being charged and possibility of facing a criminal conviction", he said.
Mr McGrath said political leaders should not just call out what they saw at the weekend, but also be "incredibly careful" at what they imply.
Northern Ireland's first minister, Arlene Foster, has urged young people not to "get drawn into disorder" and refrain from attacking police.
The police described the events as a "staged attack".
"And I send my strong support to all of the rank-and-file police officers that are on duty over this Easter weekend".
Her sentiments have been echoed by Northern Ireland Secretary Brandon Lewis who described the unrest as "completely unacceptable". He said violence was never the answer and there was no place for it in society.
'The officers who serve the Newtownabbey area are fathers, mothers, brothers and sisters, they have families who wait every day on their loved ones coming home, hoping they have not been injured, or worse'.
The disorder has flared amid ongoing tensions within loyalism across Northern Ireland.
Many pro-British unionists fiercely oppose the new trade barriers introduced between Northern Ireland and the rest of the United Kingdom as part of Britain's departure from the European Union and have warned that their unease could lead to violence.
In addition, the decision made by the Public Prosecutor Service last week not to press charges against 24 Sinn Féin politicians who breached COVID-19 restrictions by attending the funeral of former republican Bobby Storey in July 2020 has caused further anger among loyalist communities.
All the main unionist parties have demanded the resignation of Northern Ireland's police chief over the controversy, claiming he has lost the confidence of their community.