The family of murdered schoolgirl Alice Gross "remain stunned" that the foreign criminal believed to be responsible for her death was "not monitored or even known about in any way" after he came to the UK.
Her mother Ros Hodgkiss told an inquest jury on Monday that there were still "unanswered questions" over the circumstances of the 14-year-old's death.
Builder Arnis Zalkalns, who had served a prison sentence for murdering his wife in his native Latvia, is believed to have killed Alice in a sexually motivated attack.
Alice disappeared from her home in Ealing, west London, on August 28 2014. Her body was found on September 30 after Scotland Yard conducted its biggest search since the July 7 bombings.
Zalkalns was found hanged in a park on October 4 and police said the 41-year-old would have been charged with Alice's murder had he been alive.
Coroner Dr Fiona Wilcox ruled last year that the inquest, being held at the Royal Courts of Justice in London, will examine whether failures by the British Government and police contributed to her death.
Reading from a prepared statement, Ms Hodgkiss said: "It is impossible to express the devastation that we still feel at Alice's death. We have many unanswered questions. We will never know exactly what happened on that day."
She said the family was "extremely grateful" to the coroner that the issues they had raised "are going to be explored".
Ms Hodgkiss added: "We want to reiterate that the reason for these questions is so that we can establish whether or not the systems for monitoring foreign offenders and cross-border sharing of information are robust.
"We appreciate that they may have changed significantly, but we remain stunned that a foreign national with a conviction for murder was not monitored, or even known about in any way.
"This has destroyed much of our faith in our country's ability to protect its citizens.
"The Home Office and the police forces nationwide should be doing everything they can to ensure that this should not be allowed to happen again."
Ms Hodgkiss described her daughter as a "lively, popular and compassionate girl with many friends".
She said: "She was witty, smart and academic, but she could also push boundaries. In this way she was no different to any normal teenager.
"She was independent and like many teenagers of her age she enjoyed shopping, cinema and attending parties with her friends."
Ms Hodgkiss added: "She could also at times be shy and under-confident and she cared a lot about what other people thought of her.
"She wanted to be cool and she had a very individual and striking fashion sense."
She told the coroner and the jury that Alice was a "very good musician and she hoped to become a singer-songwriter".
The inquest continues on Tuesday.