Speaking during Sunday morning service at the Presbyterian Church in Pomeroy, Co Tyrone, yesterday morning, the minister, the Rev William Bingham, called on the Orangemen to "back off" from their Drumcree protest.
Mr Bingham, deputy Grand Chaplain of the Orange Order and County Grand Chaplain of Armagh, said: "I'm not ashamed to say that I wept as I heard of the loss of three little boys burned to death in Ballymoney."
He continued: "To make it worse, perhaps those who did it would say that they did it for the cause of Orangeism, in the name of Orangeism, and for the sake of a parade at Drumcree.
"Whatever reason they did it, they could never say they did it for Orangeism because it is exactly the opposite of what Orangeism stands for. It is anathema to Orangeism and it ought be so, and will be declared to be so today, I hope, at every Orange service taking place throughout our land today.
"On Thursday, having visited the Prime Minister, in a television interview I said that no road is worth a life - let alone three lives of three innocent little boys.
"I believe wholeheartedly in the principles of Orangeism. I believe in civil and religious liberties for everyone. I believe in the right of Orangemen to walk.
"But I have to say this. That after last night's atrocious act, a 15-minute walk down Garvaghy Road by the Orange Order would be a very hollow victory. Because it would be in the shadow of three coffins, of little boys who wouldn't even know what the Orange Order was about."
Mr Bingham said if the order couldn't control its protests it should not call its people on to the streets.
After the fatal incident, two things needed to be done: residents' groups uninterested in accommodation should be stood down, and secondly the Orange Order needs to call off its protests, "because we can't control them. Drumcree is rapidly getting out of our hands. We have to back off from that."
The Grand Orange Lodge described the killings as a "dastardly crime" which was "sadly symbolic of the cancer of sectarianism in our land".