The speech, delivered during a state dinner hosted by Irish President Mary McAleese, was her only scheduled comments during a four-day visit to Ireland.
While she did not apologize for British actions during the conflicts, she said it was clear mistakes were made.
She proposed a toast to the people of Ireland, then said, "I love these clinking glasses," after the champagne flutes were raised and clinked.
The queen visited Croke Park, the site of the 1920 British massacre of Irish civilians known as "Bloody Sunday." The large sports stadium is a revered spot for Irish nationalists who mourn those who died there during the conflict with Britain.
"Bloody Sunday" has never been forgotten, but the queen's visit was seen by some as a step toward healing.
Queen Elizabeth II's decision to make an appearance in Croke Park was part of her larger plan to use this trip to show understanding of the issues that have often separated these two neighboring countries.
The queen also laid a wreath at the Irish National War Memorial. She is the first reigning British monarch to visit Ireland.
The Associated Press contributed to this story