After Breck's death, the Surrey force referred itself to the Independent Police Complaints Commission, which is conducting an inquiry. Breck's parents are also suing Essex police, accusing them of failing to share information with Surrey police about the case.
LaFave said: "I want Breck's tragedy to open the eyes of everyone to recognise the dangers of online predators. It is a very real danger today."
The Breck Bednar Memorial Foundation had been set up to raise money and awareness to help protect children, she added.
It is understood Daynes and his victim met after they played online video games together. Barrister Richard Whittam, QC, told the court it was the prosecution's case the murder "involved a sexual and sadistic motivation".
Family members said Breck, from Caterham in Surrey, left home after arranging to meet a friend. He was found more than 50km away in Grays on February 17 with a fatal stab wound to the neck.
LaFave and the victim's father, oil futures trader Barry Bednar, originally from Houston, Texas, were both in court to hear Daynes' plea.
Daynes will be sentenced on January 12.