"I hope that this is the last time that anybody has to suffer what I have suffered as a result of what happened to Steve," she said.
"If Steve's death has made a positive effect on all this, that is all I care about. It's a hard lesson for everybody to learn but ... I don't want Steve to have died in vain."
Liam Stevenson, a Catholic canon who led the funeral service, told the mourners that both attacks were "designed to destabilise the peace process".
"We will not lose the peace, because so many people are so determined to move forward,'' he said, adding that the attacks had brought the community together.
Among the mourners at the Roman Catholic Church of Saint Therese were politicians from Sinn Fein, the IRA-linked party, that had never attended a police funeral before.
Shaun Woodward, Britain's Northern Ireland secretary, and Dermot Ahern, Ireland's justice minister, also attended.
Hugh Orde, Northern Ireland's police chief, who addressed the mourners, said "we will not forget him [Carroll]".
A service for Mark Quinsey, 23, and Cengiz Azimkar, 21, the two British soldiers killed last Saturday, was held at the Massereene barracks.
Attackers opened fire on the soldiers on Saturday night as they collected pizzas outside their regiment's headquarters in Massereene.
Gordon Brown, the British prime minister, said their killings would not affect the Northern Ireland peace process.
Leaders from both sides of the political spectrum have condemned the attacks and vowed that they would not harm the power-sharing government which came into effect in 2007.