Last night the Home Office said that it would apply to appeal the judgement.
A spokesman for the Home Office said: "The protection of children and vulnerable groups must not be compromised.
"We are disappointed by this judgment and are seeking leave to appeal to the Supreme Court."
But experts warned that there was no guarantee any appeal would be granted, given the judgement was handed down by Lord Dyson, who is the second most senior judge in England and Wales.
If the judgment does go to the Supreme Court, it will mean that any changes the system are on hold for up to a year while lawyers prepare.
Ministers could change the law to 'filter' out any old or minor conviction information which did not lead to a term in prison from criminal record checks if they lose.
Another option is for the Government to do nothing and require employers to weigh up whether they are breaching a job applicant's human rights when they have seen the misdemeanours on his or her CRB certificate.
The appeal court made the ruling in the case of "T", a 21-year-old man who received warnings from Greater Manchester Police when he was 11 years old in connection with two stolen bicycles.
This information was disclosed on two occasions: when he applied for a part-time job at a local football club at the age of 17 and later when he applied for a university course in sports studies.
Liberty's legal officer, Corinna Ferguson, said: "This sensible judgment requires the Government to introduce a more nuanced system for disclosing this type of sensitive personal data to employers.
"For too long irrelevant and unreliable information provided under the blanket CRB system has blighted people's lives. We hope that long overdue reforms - properly balancing the aim of public protection with privacy rights - will now be forthcoming."
John Wadham, Chief Legal Officer at the Equality and Human Rights Commission, which also intervened in the case, said: "Many of us have been in minor trouble with the law as children, which we regret at the time but we would not expect that to affect our ability to get a job later in life.
"The fact that the court has made a declaration of incompatibility indicates the seriousness of the contravention of human rights obligations in this case, which Parliament must now correct without delay."
Mike Pemberton, a partner and head of the Civil Liberties Unit at Stephensons Solicitors who represented "T", said: "This is a case where human rights equals common sense. You can't argue that something you did when you were 11-years-old will blight you for the rest of your life.
"It defies common sense that a minor caution at the age of 11 should have to be disclosed on every application for a job of certain types in the future. My client undergoes the rigmarole of having to explain the matter again and again."
Speaking after the ruling, Falklands veteran Simon Weston told how a conviction for being a passenger in a stolen car as a teenager had "haunted his adult life".
Last year Mr Weston was forced to pull out of standing to be an elected policing and crime commissioner because of the conviction.
Mr Weston, who was fined for his transgression, said the current rules led to "so many good people" being written off and was pleased that "legal minds agree".
The 51-year-old said he withdrew from the elections for the £100,000-a-year policing role in South Wales after he was "hounded" over the offence.
He said: "I told the truth, then I was getting hounded by one or two people telling me I definitely can't stand. It was when I was 14, I'm 51 now. How long must this mistake haunt my life?"
Mr Weston, a father of three and a former Welsh Guardsman, was badly burned when the RFA Sir Galahad was destroyed in 1982 during the Falklands conflict.
He suffered 46 per cent burns on his body and underwent 70 separate major operations or surgical procedures during a slow recovery.
Mr Weston overcame his injuries and went on to forge a new career as a charity worker, writer of children's books and after dinner speaker.
"How many people didn't pinch a pack of sweets at the age of 10 or 11-years-old? We all make ridiculous mistakes before we're 16-years-old. We're going to write off so many good people."