Michael Gallagher, whose son, Aidan, was killed in the bombing, said the case had been a disaster for the Omagh families.
"I think there has to be real questions why this was allowed to go through the system.
"The police recommended the prosecution and the DPP allowed it to move forward, then they brought us all here for Christmas to get this news."
He said both the British and Irish Governments must now set up a full cross-border inquiry into the Omagh bombing.
"They can no longer refuse to give families such an inquiry. This case has been a disgrace by any standards."
The father of a 12-year-old boy killed in the bombing blamed Northern Ireland's former police chief for the acquittal.
English lawyer Victor Barker, whose son, James, died in the attack, said: "It is the appalling inefficiency of Sir Ronnie Flanagan that has meant Chief Superintendent Baxter has not been able to secure a conviction."
He said the initial investigation by Sir Ronnie had been deeply flawed.
Mr Barker added: "He said he would fall on his sword if anything was wrong with this investigation — I will give him the sword."
Mr Barker, who attended the court with his wife and 13-year-old son, Oliver, said they were "very disappointed" at the judge's decision which had to be based on the evidence put before him.
But he added: "It is my view and the view of my family that Sean Hoey was one of the conspirators involved in the Omagh bomb — we can't prove it."
He said that, as a lawyer, he accepted the legal system was there to protect the human rights of people such as Sean Hoey and he had to stand by it.
"It is only a great shame that my son and the 29 people who died in Omagh has no human rights at all."
Mr Barker appealed to organisations such as the Real IRA to put the past behind them or there would be "no future for this island".
Lawrence Rush, whose wife died in the bombing, also hit out at what he said was the devastating way the investigation had been mounted.
He revealed he had taken legal action against the police over their handling of evidence and the way some of it had been lost.
He said: "I am tired, I am exhausted after 10 years of pain and hope."
But he added: "I am not over-disappointed, I would not have wanted the wrong man to be convicted."
Stanley McCombe, whose wife, Ann, 48, was another of the victims, said he was shocked by the decision.
He added: "I'm flabbergasted, dumbfounded. I do not know what to think. All the resources over the last nine and a half years have not got us anywhere.
Hoey has done four and a half years and I'm sure his compensation will be far greater than we had to fight and embarrass ourselves into getting."
Meanwhile, senior police officers involved in the investigation, including Chief Superintendent Norman Baxter, said they accepted the court decision and it was deeply regretted that many of the victims and their relatives had not seen anyone brought to justice for the crimes.
Police would study Mr Justice Weir's judgment in detail and would work to ensure that any organisational or procedural shortcomings were addressed.
A statement said: "Our primary focus will continue to bring all those responsible for these crimes, most notably the Omagh bombing, before the courts.
Our investigations will continue and we would ask anyone with information about these crimes to come forward."
PA