The 33-year-old from Trillick, Co Tyrone was given a life sentence last month for killing and sexually assaulting the little girl.
He was described as an evil sadistic killer by prosecution QC Ciaran Murphy, who said McCarney should be given the highest tariff for murdering the 15-month-old baby in December 2009.
Mr Murphy said McCarney, of Woodview Crescent, had subjected Millie to gratuitous violence from which he had gained satisfaction.
He said it was accepted by the defence that given the vulnerability of Baby Millie, that the higher starting point in any tariff applied.
He added that violence and sexual maltreatment was gratuitous and inflicted in an evil and sadistic way, an evil infliction of injury on a fragile vulnerable youngster for no other purpose, motive or aim other than to gain some form of satisfaction.
The murder of a child could attract a tariff of up to 20 years, but counsel for the defence, Elis McDermott, said there was no evidence to support that her client had acted in a sadistic manner.
She argued that McCarney should only be sentenced for the crimes of which he was convicted.
In her counter-argument Ms McDermott said as regards motive, she wanted to make it clear that Mr McCarney does not accept responsibility for any of the offences of which he was convicted.
The question of motive, said the defence lawyer, cannot always be established, as was the question of gratuitous violence.
Ms McDermott submitted that while in some cases it was clear what the motivation was, in this case the evidence just did not reach that standard.
Mr Justice Stephens has reserved judgement on the tariff to be imposed in the case, as he said it was a difficult case with a number of complex and convoluted issues to be resolved.
But after the ten week trial last year, the same judge warned McCarney that for his "despicable crime... you for your part should understand, you are going to prison for a very long period of time".
Baby Millie's mother, Rachael Martin sat at the back of the court with her mother and stepfather.
Martin, of Main Street in Kesh, was acquitted of neglect and allowing the death of her daughter.