Levi Bellfield, 45, was convicted in 2011 of the kidnap and murder of the 13-year-old in Surrey. He was already serving life for two other murders.
Bellfield took legal action after being attacked by a prisoner with a makeshift weapon at Wakefield Prison in 2009.
The Ministry of Justice (MoJ) said it was “hugely disappointed” by the court’s decision.
Bellfield, from London, claimed he suffered minor injuries in the attack and that prison staff should have protected him.