The family of Barnaby Webber, one of three people killed in a series of knife attacks in Nottingham last June, have said they "fully support" calls for a public inquiry.
"Questions must be asked, answers must be given and, where appropriate, lessons must be learned," they told Sky News.
The family of the 19-year-old student will be meeting Labour leader Sir Keir Starmer on Tuesday after he added his voice to calls for an inquiry.
Valdo Calocane was sentenced to a high-security hospital after he killed Mr Webber, another 19-year-old student, Grace O'Malley-Kumar, and a school caretaker Ian Coates last year.
Speaking after the 32-year-old was sentenced on Thursday, Mr Webber's mother, Emma Webber, told Nottinghamshire Police "you have blood on your hands".
James Coates, the son of Ian Coates, who was 65, said the killer had "got away with murder".
There were a series of missed opportunities to prevent the killings.
Calocane had been detained in hospital four times, while a warrant for his arrest was issued months before his deadly rampage. He pleaded guilty to manslaughter on the grounds of diminished responsibility.
The sentence could be referred to the Court of Appeal after the attorney general received a complaint arguing it was too lenient.
Speaking outside Nottingham Crown Court after the sentencing, Ms Webber said: "True justice has not been served today. We as a devastated family have been let down by multiple agency failings and ineffectiveness."
The family feels "even more pain now that we know how truly dreadful the events of that night were", Ms Webber told the Daily Mail.
She added: "We are drained, exhausted and broken but we now have a fight on our hands to find out what went wrong."
Barnaby, who loved cricket, texted his mum for the last time after scoring 50 while playing for Nottingham University.
"Sometimes I let myself pretend he's just at university," Mrs Webber said.
"In the summer, I used to pretend he was out playing cricket because it gave my brain a rest for a moment.
"The pain was so physical and visceral.
"Barney should have been 20 on 11 January. I have so much anger now that he's not here - that his future has been stolen so senselessly, so cruelly."