Although she stopped short of offering an apology, the Queen said the two islands could "never forget" the victims.
She also made a direct reference to the murder of the Duke of Edinburgh's uncle, Lord Louis Mountbatten, by the IRA, as she told the dignitaries that the events of the past had "touched us all, many of us personally".
"Of course, the relationship has not always been straightforward; nor has the record over the centuries been entirely benign," she said.
"It is a sad and regrettable reality that through history our islands have experienced more than their fair share of heartache, turbulence and loss.
"These events have touched us all, many of us personally, and are a painful legacy. We can never forget those who have died or been injured, or their families.
"To all those who have suffered as a consequence of our troubled past I extend my sincere thoughts and deep sympathy.
"With the benefit of historical hindsight we can all see things which we would wish had been done differently or not at all."
The Queen applauded the work of all those involved in the peace process, and who continue to work for peace today.
"The lessons from the peace process are clear. Whatever life throws at us our individual responses will be all the stronger for working together and sharing the load," she said.
The Queen is the first British monarch to visit the Republic in 100 years. Earlier in the day she visited Croke Park, the Gaelic football and hurling stadium and site of the original 'Bloody Sunday', where British troops opened fire on the crowds as they watched a match in 1920, killing 14 innocent people.
In a symbolic gesture, she observed a minute's silence after laying a wreath at the Irish War Memorial Garden in Dublin in honour of the 50,000 Irish soldiers who died fighting alongside the British in World War I.
Her visit has been hailed a great success by the Church of Ireland.
Its Primate, Archbishop Alan Harper, said: "I rejoice that relationships between the Republic of Ireland and the United Kingdom have so changed as to make the visit of Her Majesty possible."
He praised the "tireless" efforts of President McAleese and her husband Martin in "seeking to break down barriers and heal divisions in both parts of Ireland".
"I also pray earnestly, 'on my knees', that those who remain discontent with the current political accommodations on this island my turn away permanently from violence and bloodshed and play their part in enabling the processes of peace and reconciliation to come to a richer fruition," he said.
A spokesman for the Church of Ireland added: "The Church's response [to the Queen's visit] is very positive. It's going very, very well."