Richard and Ann Craig, whose 14-year-old son Euan died following an attack before a PE class at Rosshall Academy in Crookston in May, have vowed to push for a fatal accident inquiry into their son's death.
The couple had called on the Crown Office to challenge a judge's decision to lock up the boy who killed their son for three-and-a-half years.
The teenager responsible, who cannot be named for legal reasons, is expected to be freed in less than two years under automatic early release.
Lord Advocate Frank Mulholland informed the Craig family shortly before Christmas Day that the sentence would not be appealed.
Richard Craig, 44, has said he is "disgusted" with the decision, adding: "I was seething after sentence was handed down.
"I raised it with the Crown but they seem to think 42 months is fit and proper punishment for killing someone.
"I think the sentence is laughable. We feel very let down by the judicial system. At times we were made to feel that we shouldn't challenge the Crown, but they seem to forget they are public servants."
Euan died after a pupil turned on him after being accidentally struck by a sponge ball as the class waited outside a gym hall.
The boy repeatedly punched Euan in the head, despite the vcitim's repeated apologies. Euan suffered a seizure after the attack and died the next day in hospital.
His killer pled guilty to culpable homicide at the High Court in Glasgow in October.
Euan's father has also criticised judge Lord Bracadale for commending his son's killer for admitting guilt, and the school for failing to explain why his son's class was not attended by a teacher at the time of the incident.
He said: "There was no other avenue for my son's killer but to admit guilt because there were 26 witnesses.
"I'm hearing that classes are still unattended at Rosshall Academy.
"I'm looking for a fatal accident inquiry."
A Crown Office spokeswoman said: "While the Crown does have a right to appeal against unduly lenient sentences, the appeal court has set a strict legal test which must be satisfied before a Crown appeal against a sentence can be successful.
"Following full and careful consideration of all of the facts and circumstances in this case, Crown counsel concluded that that test could not be met in this case.
"Accordingly there will be no Crown appeal."