PSNI held a meeting with victims relatives and UUP MLA Tom Elliott on Friday and informed them they had completed their inquiries as part of a review and would not be continuing their probe.
"Police would continue to appeal to anyone with information to come forward so that the people responsible for this atrocity are brought to justice," a spokesperson said.
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.
A car bomb exploded outside a pub on the town's Main Street, instantly killing a woman, man and nine-year-old girl, and fatally injuring two others.
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.
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.
Claudy is often referred to as the forgotten atrocity.
Tom Elliott, UUP
Justice for Innocent Victims of Terrorism, which represents a number of the Claudy families, expressed deep disappointment reiterated the public appeal for information.
"Claudy was an act of vicious terrorism which was directed against the entire community," a spokesperson said.
"To think that over 41 years have passed since this high profile bombing yet no-one has yet been brought to justice or held criminally accountable is an indictment of not only our criminal justice system but also of a community which wilfully harbours those responsible."
They continued: "JIVT Ltd along with Claudy families has been advancing alternative processes which seek to bring justice and truth which up until now has been denied those affected. In the upcoming weeks and months, this work will intensify; there exists a resolve amongst many that justice and truth must prevail.
"Claudy is a particularly complex case with a number of institutions standing to face very difficult questions about their actions, or indeed their inactions, on a number of levels.
"Claudy was a crime against the community perpetrated by the Provisional IRA and it is essential that those responsible are held publicly and personally accountable for their actions."
UUP justice spokesperson Tom Elliott expressed frustration that the investigation has been halted.
"The news that the Police have suspended the investigation due to a lack of evidence and information was met with a mixture of frustration and anger," the Fermanagh and South Tyrone MLA said.
"The investigation into it has been a catalogue of failures right from the start.
"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."
He concluded: "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."
Mr Elliott said he would be calling for an immediate meeting with Chief Constable Matt Baggott to explain the handling of the case.
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."