Norrie and Claire Aitchison said that Liam's killers should have been kept in custody before and during their trial.
The Aitchisons said they will campaign to have the rules changed.
On Monday, Johnathan MacKinnon and Stefan Millar, both 22, were convicted of murdering Liam.
The two men had lived on Lewis.
Following their arrests in December 2011, Millar was allowed bail and moved to Inverness. MacKinnon was bailed in February 2012.
A jury at the High Court in Glasgow convicted the two men of murder.
The court had heard that Liam was beaten, stabbed and stripped his of clothing during an attack on 23 November 2011.
The body of the 16-year-old, from South Uist, was later found in a derelict property in Steinish on Lewis.
Following the conviction of the two men, Mr and Mrs Aitchison have spoken out against the right of murder suspects to bail.
They said the knowledge that MacKinnon and Millar were out on bail had caused their family distress.
Mr Aitchison said his youngest son, Steven, eight, had shared a room with Liam when he stayed at home and was terrified after his older brother was murdered.
He said: "The wee fellow wouldn't sleep and thought he was next - we had to move him from the downstairs room to the upstairs room because the downstairs room was by the front door.
"He had to watch us lock the door and if I wasn't in he had to wait until I was before he would go to sleep"
"We want to head up a campaign to keep anyone that is charged with murder on remand until proven innocent or guilty."
The Aitchisons said that they also hope to set up a memorial garden for Liam.
The father and step-mother of murdered Western Isles teenager Liam Aitchison have called for bail to be refused to people who are charged with murder.