Dermot McShane died after an armoured Army vehicle drove into hoardings he was sheltering behind during disturbances in Londonderry in 1996.
His American widow Treasa was awarded £8,000 by the judges on Tuesday.
She brought civil proceedings against the Ministry of Defence, the former chief constable of the Royal Ulster Constabulary and the Northern Ireland secretary for alleged negligence and breach of statutory duty.
Mrs McShane said her husband was killed, either intentionally or by unnecessary force, by soldiers.
The Committee on the Administration of Justice said the judgement was a significant step towards protecting rights in Northern Ireland.
The Belfast-based human rights group took on Mrs McShane's case.
'Alleged responsibility'
Legal officer Paul Mageean said: "It is a salutary reminder to government that, even in the midst of conflict, the state and its agents must act within the rule of law."
The government said Mr McShane's death was a "tragic accident" and did not with breach the Human Rights Convention.
The court made no findings about the alleged responsibility of the state for Mr McShane's death.
However, it said there were failings in the investigation into his death.
It said investigating officers were not independent of those implicated in the incident and the investigation "lacked expedition".
'Made documents available'
The judges also criticised the fact that the soldier who drove the vehicle which fatally injured Mr McShane could not be ordered to give evidence at his inquest.
"The court therefore held that there had been a violation of Article 2 concerning the lack of an effective investigation into Mr McShane's death," said the judges.
They said the government was also found to have breached the Human Rights Act after police alleged a solicitor made documents available for the applicant's case to the European Court.
The European Court said the state's actions in bringing the complaint could have a "chilling effect" on those taking cases.
In a statement, the Northern Ireland Office said: "The judgement does not highlight anything that was not raised in May 2001.
"Since then, the government has put together a package of remedial measures which should address the court's concerns."
Sinn Fein chairman Mitchel McLaughlin said the decision was "just the latest in a litany of findings against the British government surrounding civilian deaths" in Northern Ireland.