Child killer Ian Huntley was a "timebomb ready to go off", Jessica Chapman's father has said.
Sharon and Leslie Wells welcomed Huntley's conviction
Leslie Chapman said his daughter and her best friend, Holly Wells, were simply in the "wrong place at the wrong time" when they were killed.
After Huntley was handed two life sentences for their murders, Mr Chapman said the next time he sees the former school caretaker he wants him to be "in a coffin".
Speaking at the same news conference Holly's father, Kevin, said the revelation that Huntley was well known to the police for suspected sex offences "impacted very negatively on us".
Mr Wells said that he and his wife, Nicola, hoped to take part in a review of vetting procedures for people applying for jobs with children.
Neither family expressed anger at the system of checks which allowed Huntley to get a job as a school caretaker, despite being accused of having sex with underage girls and of rape several times in the past.
Kevin and Nicola Wells will help an inquiry into Huntley's appointment
Mr Chapman welcomed moves to introduce tighter checks, but added: "You are always wiser after the event."
The 52-year-old also called on Huntley to have "the guts" to properly explain what happened on the night he killed their daughters.
He said: "Our life sentence started last August, his is only just beginning."
Kevin Wells welcomed the guilty verdicts against Huntley and Maxine Carr, who was convicted of conspiring to pervert the course of justice, but added: "There was certainly no sense of euphoria".
He went on: "We have had doubts for 16 months... Not until that verdict was
announced today have we had a cessation of our fears."
Asked whether he would like the death penalty reintroduced to deal with such cases, Mr Wells declined to comment.
The two families praised the police, family members and friends who had helped them through their ordeal.
Mrs Chapman and Mrs Wells spoke little during the news conference.
But when asked to describe how they remembered their daughters, Mrs Chapman said: "Loud, noisy and a real tomboy."
Mrs Wells, 36, said: "Happy, no worries and enjoying life."
Sharon Chapman, 44, said the support from the people of Soham had been "amazing".