Richard and Gloria Taylor demanded further action against three unnamed scientists from the Government's Forensic Science Service (FSS), whom they accused of making "basic mistakes".
Inquiry: 'Human error' behind forensic mistakes in Damilola Taylor case
The couple said they were enormously disappointed with the "dreadful errors" exposed in an official report commissioned by the Home Office.
The Taylors' solicitor, Neil O'May, said: "They believe that those responsible for these dreadful errors should be brought to account so that nothing like this could ever happen again. The report describes the catalogue of errors as 'extremely regrettable' - a conclusion that the family feel is lame in the extreme. The Government should instead now act decisively to overhaul the quality of forensic science used in court."
Damilola bled to death in the stairwell of a block of flats in Peckham, south London, in 2000 after suffering a single stab wound to his leg, probably from a broken bottle.
Danny and Rickie Preddie, aged 18 and 19, were convicted of Damilola's manslaughter at a second trial in August last year, the third to be staged over the killing.
The inquiry into the FSS's mistakes found they was down to "human error" rather than a failure in the system as whole. Conducted by forensic expert Professor Brian Caddy and top barrister Alan Rawley QC, it said three FSS experts "failed to recover crucial evidence".
The report said that a new FSS service, in which items are examined twice by separate forensic scientists, should be adopted by police in major cases despite the extra cost. The new double-checking service would have added just £55,000 to the overall cost of the Damilola investigation.
Other recommendations were that each FSS laboratory should be evaluated at least once a year by specialist teams within the organisation, and there should be more emphasis on close co-operation between scientific officers and their supervisors.
Home Office minister Joan Ryan said: "I would like to express my sincere apologies to Damilola Taylor's family and acknowledge the further distress this has undoubtedly caused them." She would give full consideration to the report's recommendations after receiving a response from the FSS, she added.