BBC Scotland revealed on Thursday that council chief executive Angela Scott excluded herself from the inquiry which led to a secret report shown to councillors this week.
Tommy Campbell, from the Unite union, said more transparency was needed.
The convener of the council's finance committee said he had "full confidence" in the chief executive.
BBC Scotland revealed in 2013 that no ashes had been offered to the families of infants cremated in Aberdeen over a five-year period.
Baby and adult ashes were mixed together and given back to relatives of the adult, while the parents of infants were told there were no ashes.
It followed similar revelations about Mortonhall crematorium in Edinburgh, which had been secretly burying baby ashes for decades.
A report into the scandal by Dame Elish Angiolini described the practices as "abhorrent".
The council director responsible for Hazlehead Crematorium in Aberdeen, Pete Leonard, did not attend Wednesday's council meeting to discuss the secret report commissioned by Ms Scott. He was said to be on annual leave.
Ms Scott showed the report to councillors on Wednesday, but then took it back citing legal advice.
The authority confirmed that she asked for the investigation to examine managers' actions only up to director level.
That excludes the part played by Ms Scott and her predecessors.
Mr Campbell, from Unite, warned of an "institutional denial of problems".
He said: "We were absolutely shocked to discover that she and previous chief executives were not subject to questioning as a result of the recent inquiry.
"We are wanting to know were councillors aware of this?"
The union has written to Ms Scott.
Councillor Willie Young, convener of the finance policy and resources committee said he was "disappointed and saddened" by Mr Campbell's intervention.
He added: "I have full confidence in the chief executive to act in the public interest at all times.
"I also believe Mr Campbell is wrong to suggest that there is a culture of favouritism operating within certain sections of the city council."
A union has called for a new probe into the handling by senior council managers of the baby ashes scandal in Aberdeen.