Around 90 people who were sexually and physically abused by their carers in Jersey children's homes will receive compensation of up to £60,000 after the government in St Helier offered an "unreserved apology" to the victims.

Announcing the launch of a "historic abuse redress scheme" on Thursday, Jersey's chief minister, Ian Gorst, acknowledged "that the care system that operated historically in the island of Jersey failed some children in the states' residential care in a serious way".

At least 43 of the victims set to receive compensation were mistreated at the Haut de la Garenne care home, which in 2008 became the centre of a criminal investigation into historic child abuse allegations. Police excavated the grounds of the home after receiving tip-offs that children could have been murdered and buried under the building.

No human remains were ever found and Jersey police subsequently admitted that their initial inquiry was flawed. But behind the scenes and away from the headlines, police were still investigating more than 100 allegations of serious child abuse at the home.

By the time the historic inquiry was closed in December 2010, eight people had been prosecuted. These included Michael Aubin, who admitted abusing young boys in the 1970s while he was a resident at Haut de le Garenne. Gordon Claude Wateridge was sentenced to two years in jail in 2009, aged 78, after being found guilty of eight indecent assaults and one common assault.

One woman who was sexually abused by a carer at the home for at least three years in the 1970s said on Thursday that it was "about time" the states of Jersey accepted responsibility for the abuse meted out by its employees at Haut de la Garenne over such a long period.

The woman, who did not want to be named, said in a phone interview: "Compensation is probably the wrong word because you can't give people their lives back, but the only way we can be compensated for what happened is with money."

She said the Jersey authorities were slow to react to allegations of abuse and had until now not apologised for the agonies inflicted on so many children in their care. But the money went a little way towards showing regret. "Money is all they understand in Jersey," said the woman, who is now in her 50s.

Last year, along with 42 other victims, she launched a case for compensation at the high court in London after their complaints were ignored in Jersey. This action will now be discontinued in the light of the compensation.

The woman was sexually abused by a male carer from the age of 13 until after her 16th birthday. It later emerged that he had been convicted of having unlawful sex with a minor before getting his job at the Jersey home, and after leaving the island he was convicted of child sex charges at a school. The woman said it took her until the mid-1990s to pluck up the courage to report the abuse to Jersey's children's services department – and that her allegations were not taken seriously enough. "They never gave me any indications that I wasn't the only one," she said.

The woman questioned the motives of the Jersey administration in announcing the compensation scheme. "I think they realise they were morally culpable, but the main thing is that they don't want any more embarrassment," she said. "They don't want to have it all dragged out and have reporters digging around again – it's not good for the island."

There was outrage in 2008 when the former chief minister Frank Walker was caught on microphone saying that one of the island's politicians, Stuart Syvret, was "trying to shaft Jersey internationally" by acting as a whistleblower in the abuse inquiry.

Alan Collins, a lawyer who represents 43 victims, said: "No amount of compensation can ever put right what the these children endured, but no matter how imperfect the means to achieve justice, what matters is the fact that the states of Jersey has recognised the need to do the right thing".

To claim compensation from the Historic Abuse Redress Scheme, victims have to prove that they were abused while in the island's full-time residential care at any time between 9 May 1945, the day Jersey was liberated from its Nazi occupation, and 31 December 1994.