Former Lord Advocate Dame Elish Angiolini said the results of her year-long investigation, published yesterday, would "cause more pain and distress" for most of the 253 families involved.
The remains of foetuses and small babies were secretly buried at the City of Edinburgh Council facility over more than four decades, despite their families being told there would be no ashes following cremation.
In her long-awaited report, Dame Elish concluded that, while the remains of some babies were buried in a garden of remembrance, ashes from others had been mixed in with the remains of adults.
On other occasions, they had been vacuumed up and buried in another area next to skips and tractors.
Dame Elish said: "It cannot be said with any certainty what remains of which babies are interred in the Garden of Remembrance.
"The great tragedy of these events over many years is that many parents will now be left with a lifetime of uncertainty about their baby's final resting place."
Bereaved parents called for a full public inquiry following the publication of the findings, which contained 22 recommendations.
The Scottish Government, which has appointed an independent commission chaired by former high court judge Lord Bonomy to look at practices across Scotland, said it was committed to changing the law regarding cremations and that a wide-ranging bill was planned.
The report into Mortonhall practices between 1967 to 2011 found that former superintendent Anne Grannum and bereavement and public health manager George Bell had mistakenly believed it was impossible to obtain ashes from babies and ignored evidence to the contrary.
The investigation found "overwhelming evidence" that foetal bones do survive cremation.
Former cremation assistant Hazel Strachan told the investigation that, on occasions where remains were found, Ms Grannum ordered families should not be informed as it would be "too distressing" for them.
Although Ms Grannum disputed the evidence, Dame Elish said she found Ms Strachan to be "reliable and credible".
Dorothy Maitland, operations director of the bereavement charity Sands Lothians and one of the affected parents who helped expose the scandal, said she felt "total devastation".
"My daughter's ashes could be in the garden of remembrance, she could be next to a skip or she could be in someone else's urn," she said. "I also feel very let down by a previous manager at Mortonhall - he blatantly told me on many occasions, 'You don't get ashes from a baby'. He seemed so genuine, I feel really let down. Worse than that, I feel like I've let my baby and my family down. We have wandered for years around Mortonhall wanting to put flowers down but didn't know where to put them."
Madelaine Cave's daughter Megan Heather died in 1994 at 15 days old. She said: "In reading the report it's clear that there were remains for Megan."
Arlene McDougall, who lost her son Fraser five minutes after he was born at 23 weeks, said she blamed Ms Grannum, who was superintendent of
the crematorium until 2011. She said: "She was the one who told me there were no ashes."
Calls for a full public inquiry into infant cremations across Scotland were supported by the Labour Lothian MSP and health spokesman Neil Findlay and Ruth Davidson, leader of the Scottish Conservatives.
While the Scottish Government has not ruled out such an inquiry, it will examine Lord Bonomy's recommendations, which he is due to publish in the coming weeks, before deciding what further action to take.
Solicitor Patrick McGuire, of Thompsons, who represents many of the families involved, said he believed "there won't be a single community in Scotland that hasn't been affected" by similar practices at other crematoriums.
Public Health Minister Michael Matheson said: "My thoughts today are with all the families affected. I can't begin to imagine how they must be feeling to not only lose a child, but then be put through the further trauma this report highlights.
"I am clear that no parent should ever have to go through a similar experience to those affected by practices like this, at any crematorium in Scotland.
"We are absolutely committed to changing the law and a wide-ranging bill is already planned. The findings from Dame Elish's report will be used to inform the wider national review, and any recommendations for government will be looked at by the commission as part of their investigation."
City of Edinburgh Council chief executive Sue Bruce extended "sincere apologies to the bereaved families" on behalf of the authority for the distress they had suffered.
She added: "Dame Elish has made many important recommendations, some of which relate directly to working practices at Mortonhall. I will be working with council colleagues and elected members to take these forward.
"It is also clear from the recommendations that there are far-reaching implications regarding cremation practices and the legislative framework not just for Edinburgh but across Scotland and the United Kingdom and I will be working with the Scottish Government and other relevant bodies to address these concerns.
"We will now consult with families and relevant organisations regarding their views on a suitable memorial.
"It is vital that we learn from this and look to the future. We must ensure that the highest possible standards are adhered to at Mortonhall and that nothing like this can happen again."