Jeane Freeman told the BBC podcast Political Thinking with Nick Robinson: “We didn't take the right precautions to make sure that older people leaving hospital and going into care homes were as safe as they could be, and that was a mistake.
"I think our failures were not understanding the social care sector well enough.”
From March to May 2020, 113 patients were discharged from hospitals to care homes after having had a positive Covid-19 test but no subsequent negative test, according to a report from Public Health Scotland.
In total, 3,061 patients were moved in that period without being tested.
People with relatives in care homes responded angrily to Ms Freeman’s comments.
Gillian Duncan, whose mother died of Covid-19 in a care home, in April called the statement “insulting”.
“Why has it taken Jeane Freeman so long to admit this?” she said.
"Families like ours want the truth. We need closure in order to manage to grieve and move on. What we have been fed so far is a smokescreen.”
Avril Morton, whose mother, 88, was discharged from hospital to a care home after testing was introduced, said: "I think many relatives deserve very real answers – this isn't just an opportunity for Jeanne Freeman in her parting shot to confess and salve her conscience.”
“I have not suffered in the way others have and have felt completely helpless. Many of the 3,000 died alone or with ‘strangers’ by their side and for relatives that can’t have been easy - so for Jeane Freeman to say what she said now is shameless.”
Selena Bundy, who also has a relative in a care home, said Ms Freeman’s comments had “only made things worse”.
"I feel the whole situation has been mismanaged from the very very top of the chain to the bottom,” she said.
"Shame on our government for allowing this to happen to some of our most vulnerable people in society.”
Alison Walker added: “It's not just about this tragic mistake at the start, it's also about the ongoing mistakes.”
“The Scottish Government has focused more on statistics than on the health and wellbeing of care home residents”, she said, resulting in a “catastrophic failure” to take responsibility.
Alison Leitch, whose mother is in a care home, said: “I’d like an apology for what has happened.
"I can see very clearly the impact this has had on my mum and it’s now left to me to pick up the pieces. My mum is collateral damage of mistake after mistake when it never had to be like this.”
An SNP spokesperson said: “The Scottish Government commissioned extensive work to review the links between hospital discharges and the impact of covid in our care homes and we have acknowledged that mistakes were made.
"The First Minister has committed to establishing a public inquiry into the handling of Covid, in which the voices of families would be heard, by the end of the year and we hope other governments across the UK will come together to support such an inquiry on a four nations basis.”