Prof Black told the court prosecution's experts had drawn an "unsafe conclusion" by stating the bones were fragments of human skull.
She said: "It's a very unsafe conclusion because I genuinely do not believe there is the evidence to support it."
She also added there was "no certainty" about which part of the body the bones originated or their age.
Cross examined by prosecutor Elwen Evans QC , Prof Black explained why she couldn't say the origin of the bones.
"They are too small, they are too damaged, there are no identifiable anatomical features," she said.
Mark Bridger denies murder, abduction and perverting the course of justice. The trial will continue tomorrow.
The parents of murdered April Jones fear that killer Mark Bridger may never reveal where the body of their daughter is.
ITV News correspondent Carole Green has covered the month-long trial of Mark Bridger at Mold Crown Court. Here she gives her personal view.
The disappearance of April Jones prompted the biggest search of its kind in British policing history.