Constable Carroll was shot through the rear window of his police car when he arrived at the scene at about 2145 GMT on Monday.
Police say they are looking for a man in a light coloured top who was seen running from the area after the shooting.
At least two houses have been searched in the nearby Drumbeg estate.
At a press conference on Tuesday afternoon, Chief Superintendent Alan Todd said the constable had given 23 years of service to the community, working with the police service.
Constable Stephen Paul Carroll, 48, was from Banbridge
"We have this morning, colleagues without a workmate, a wife without a husband, a son without a father and grandchildren without their grandfather," he said.
"It is a desperate loss ... we are working with people to provide safer communities, my question to the people who perpetrated this is 'What have they got to offer?'"
The Continuity IRA is one of a number of dissident republican paramilitary groups opposed to the peace process which have carried out bomb and gun attacks on civilians and the security forces.
There is believed to be cross-over and co-operation between the Continuity IRA and the larger Real IRA, which bombed Omagh in 1998 killing 29 people and injuring hundreds more.
Chief Constable Sir Hugh Orde called it a "sad day" for Northern Ireland's force and said the gunmen were "criminal psychopaths", but said he would not ask for the Army to help patrol NI's streets.
"I have no intention to ask the Army for routine military support, it's not necessary and it doesn't work," he said.
McGuinness: 'These people are traitors to the island of Ireland'
Sir Hugh held a joint press conference with the first and deputy first ministers Peter Robinson and Martin McGuinness at Stormont.
Mr Robinson said: "This is a battle of wills between the political class and the evil gunmen - the political class will win."
Mr McGuinness said the dissidents' actions were futile: "These people are traitors to the island of Ireland, they have betrayed the political desires, hopes and aspirations of all of the people who live on this island."
Prime Minister Gordon Brown has condemned the murderers and insisted there would be "no return to the old days" in Northern Ireland.
This is the first murder of a police officer in NI since 1998. Constable Frank O'Reilly was killed by a loyalist blast bomb during disturbances linked to the Drumcree dispute in 1998.
The last police officers murdered by republicans, RUC constables Roland John Graham and David Andrew Johnston, were shot dead by the IRA in Lurgan, County Armagh in June 1997.
Constable Carroll was the first PSNI officer to have been murdered by paramilitaries since the force was formed in 2001.
Dissident republicans tried to kill two PSNI officers in shootings in Derry and Dungannon in November 2007.
They have also been linked to a booby trap bomb which exploded under a police officer's car in Spamount, County Tyrone in May 2008.
Politicians from all parties condemned Monday's killing, which Northern Ireland Secretary Shaun Woodward insisted would not damage the peace process.
Asked if the killing was linked to the soldiers' shooting at the weekend, Sir Hugh Orde said: "I think you are giving (the attackers) credit they ill deserve.
"I think these are disparate groups, badly infiltrated and indeed many awaiting trial north and south of the border.
The first and deputy first ministers have again postponed an investment visit to the US following the murder.
In the weekend attack, Sappers Mark Quinsey, 23, from Birmingham and Patrick Azimkar, 21, from London, were shot dead at Massereene Army base, Antrim.
The soldiers were killed as they accepted a pizza delivery at about 2120 GMT on Saturday.
Four other people, including two pizza delivery men - Anthony Watson, 19, from Antrim, and a Polish man in his 30s - were injured in the attack.
One of the men is in a critical condition, another is seriously ill.
NORTHERN IRELAND SHOOTINGS
1. Sat 7 Mar, 2120 GMT: Sappers Mark Quinsey and Patrick Azimkar are killed outside the Massereene Army base, Antrim. Four other people, including two pizza delivery men, are injured. Dissident republican group Real IRA claims responsibility.
2. Mon 9 Mar, 2145 GMT: Police Constable Stephen Carroll is shot dead in Craigavon after responding to a call for help from a distressed woman. Splinter group the Continuity IRA says it was responsible.
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