Nine people were killed and a number of others seriously injured when three IRA bombs exploded in the Co Londonderry village on 31 July 1972.
The PSNI met with victims' relatives on Friday and informed them they had completed their inquiries as part of a review and would not be continuing their probe.
Mark Eakin, whose nine-year-old sister Kathryn died in the first blast, spoke of his anger.
He said: "I was very disappointed, not even disappointed - devastated at the fact that they could just say 'right, we're not doing any more of that, we're giving up'.
"I'll not be giving up, and the next ones coming behind will not be giving up either - it will never be lost or forgotten and it's not going to go away."
In 2010, a Police Ombudsman report found police, church and state colluded to protect Father James Chesney, who was suspected of being involved in the bombings.
Mr Eakin continued: "Anybody that was involved in covering up Claudy originally, we need to go back and question everybody there. I know William Whitelaw is dead, but we need to question everything they know, find out what they know, but the police need to do that.
"The police should be going to track down anybody that knows anybody that knows anything about Claudy - all I'm asking is that somebody will walk forward and take their heart in their hands, stand up and say 'yes this happened' or 'yes that happened'.
"I'd like the Chief Constable to stick to his guns."
A man and a woman also died instantly when the first car bomb exploded outside a pub on Main Street in Claudy more than 40 years ago.
A second bomb was found in a van close to the post office and, as police cleared the area, people moved towards the Beaufort Hotel, where a third device had been left in a minivan.
No-one has ever been charged with the Claudy murders.
In its report, the Ombudsman's Office said the RUC investigation into Fr Chesney - who was never questioned by police and died from cancer, aged 46, in 1980 - was "compromised" after senior officers conspired with the government and church to protect him.
He was transferred to a parish in Co Donegal, outside the Northern Ireland jurisdiction in 1973, following secret talks between then Secretary of State William Whitelaw and the head of the Catholic Church in Ireland, Cardinal William Conway.
Deputy First Minister Martin McGuinness has renewed an offer to meet with the relatives.
Meanwhile politicians have expressed frustration that the investigation has been halted.
Tom Elliott, UUP, said: "The involvement of a Catholic priest, Father James Chesney was known but covered up, and there is a strong suspicion that the involvement of others may be the reason why the full facts have never been allowed to emerge."
"Concern has been raised that many of the gaps are caused by political interference.
"It is vital that anyone who may have any information, including the deputy First Minister Martin McGuinness should come forward and disclose it to the police."
DUP MP for the area, Gregory Campbell, said: "Police have called on anyone who knows anything to come forward, for this process to have any hope of offering closure to relatives there is only one realistic prospect in achieving that closure; those who were in the IRA at the time, or who know those that were, need to come forward and reveal what they know."
TUV leader Jim Allister said: "Considering the Police Ombudsman made a finding of state and church cover-up in relation to the notorious Claudy bombing, it is astounding and utterly unacceptable that the police investigation has been abandoned.
"Such only adds to the unease resulting from the cover-up finding."
Kathryn Eakin, 9, Protestant. The youngest of the victims, she died in the blast from the first bomb on Main Street. She had been cleaning the windows of the local grocery shop which was owned by her family.
Patrick Connolly, 15, Catholic. The teenager was caught up in the first explosion outside McElhinney's pub and shop. He died in hospital just over a week later.
William Temple, 16, Protestant. From nearby Donemana, the boy worked as a milkman's helper and was killed while on his round in the village.
Arthur Hone, 38, Catholic. A married father-of-two and an insurance salesman, he died a fortnight after the bomb attack. Two of his uncles - both priests - conducted a requiem mass at his funeral.
Joseph McCloskey, 39, Catholic. A factory worker, he died instantly when the first bomb went off.
Rose McLaughlin, 52, Catholic. A mother- of-eight, the café owner died in hospital four days after the outrage.
Elizabeth McElhinney, 59, Catholic. The owner of the pub and shop where the first bomb was planted, she was serving petrol from the shop's pump when she was killed.
David Miller, 60, Protestant. A street cleaner, he was killed by the third and final bomb contained in a mini-van.
James McClelland, 65, Protestant. A street cleaner and the oldest of the victims, he died in the third explosion.