On Monday, the Court of Appeal rejected Barra McGrory's claim that the minimum term of 25 years imposed on Brendan McConville was unduly lenient.
Senior judges reserved their decision on a separate bid by the DPP to have co-defendant John Paul Wooton's tariff raised from 14 to 21 years for his role in the killing.
Both men are currently serving life sentences after being convicted of the Continuity IRA murder.
Constable Carroll was ambushed and shot dead as he responded to a 999 call at Lismore Manor, Craigavon in March 2009.
McConville, 43 and from Glenholme Avenue in the town and Wootton, 23 and from Lurgan, were also convicted of possession of an AK47 assault rifle and ammunition with intent to endanger life.
The younger man was further found guilty of attempting to collect information likely to be of use to terrorists.
A circumstantial case against them at the non-jury trial involved DNA and other evidence.
Wootton's car was held to have been near the scene and driven off within minutes of the killing. Gun residue was found on a coat linked to McConville which was later recovered from the vehicle.
Last month, both men failed in attempts to have their murder convictions overturned.
The murder itself and the way it was executed was an attack on the very heart of policing and the very heart of democracy which underpins this society.
Barra McGrory, Director of Public Prosecutions
In court on Monday, the case switched to a prosecution challenge against the sentences handed down to the pair.
Mr McGrory argued that the way Constable Carroll was lured to his death represented a significant aggravating factor.
The Director further contended that the killing came at a time when Northern Ireland's police service had gained cross-community support.
"In the circumstances of this case, it should have been a tariff of 30 years or more," he submitted.
He suggested there were significant differences between the sentencing of police killers in England and practice directions used by Northern Ireland's judiciary.
But during exchanges, Lord Chief Justice Sir Declan Morgan stressed how the guidelines have operated for the last 10 years.
Sir Declan, sitting with Lord Justices Higgins and Coghlin, ruled against the application and said reasons would be given at a later stage.
Both convicted murderers listened by a prison video link as legal attempts were made to have them serve longer behind bars.
The victim's widow, Kate Carroll, was also present in court with family and friends.
Turning to the case of Wootton, still aged 17 at the time of the killing, Mr McGrory insisted his youth was the only mitigating factor.
"There's no evidence of remorse which he could express even today," the DPP argued.
"This was a young man of some considerable determination and dedication to his terrorist cause which led to a contribution to the death of Constable Carroll."
However, counsel for Wootton countered that the absolute minimum sentence necessary for rehabilitation and public protection should be applied to someone who was still a child at the time of the shooting.
Arthur Harvey QC also emphasised that the 14-years was only a tariff, and that the Parole Commissioners will then decide when his client is ready to be released.
With the prosecution having accepted Wootton played a lesser role in the murder, Mr Harvey added: "There's an unbridgeable moral gap between the person who carries out the shooting and a young man who, for whatever reason, is involved in a peripheral way."
Following submissions, Sir Declan pledged to give a decision on the application against Wootton as soon as possible.