"It is well documented you faced a vicious campaign by republicans," he said.
"Tragically, the local cemetery bears testimony to the sacrifice paid by so many people, and in particular members of the Orange Institution.
"During the Troubles we had 336 members murdered – almost entirely by republicans. More than half of them were singled out because they were serving their community in the security forces. Others were targeted simply because they were Protestant and members of the Orange Order."
Mr Stevenson has been head of the organisation for seven years.
In his address he noted when he took up the role he made a pledge to the innocent victims of the Troubles that their families would remain a key priority for the organistion.
He went on to hit out at what he said was an effort by republicans to "rewrite history to make it look as if their campaign of murder was somehow justified".
He added: "We remain proud of our traditions and cultural heritage - we have no need to apologise for them.
"I ask everyone here to keep holding their head high and to play their part in shaping the future of our great country."
On Thursday, an estimated 30,000 Orangemen took part in parades across Northern Ireland.
Around 250,000 are thought to have attended the 17 Twelfth venues.
The events mark King William of Orange's victory over James II at the Battle of the Boyne in Ireland in 1690.