Speaking at a Covid-19 media briefing on Tuesday, Ms Sturgeon declined to apologise for the decisions made, but said that a public inquiry would take place.
Her comments come after health secretary Jeane Freeman admitted last week the Scottish Government had made “mistakes” in its transfer of thousands of elderly patients from hospitals to care homes in the first months of the pandemic.
From March to May last year, 113 patients were discharged from hospitals to care homes after having had a positive Covid-19 test, but no subsequent negative test, while in total during that time 3,061 patients were moved without being tested.
Ms Sturgeon said: “Back in late February into March last year we were faced with a horrendous situation, with horrendous decisions that flowed from that.
"We were watching pictures on our televisions of hospitals in Italy being overrun by Covid and we didn’t have the hindsight that we have now.
“We thought it was wrong to leave older people in hospitals that were about to be overrun with Covid. We thought they would be safer in other settings with the right infection protection procedures and isolation procedures in place and we didn’t know what we know now about asymptomatic transmission.”
Ms Sturgeon said it was “inevitable” the government would get things wrong it its handling of the crisis.
"We tried to make the best decisions, but we would have got things wrong, it’s inevitable given what we were dealing with, but that doesn’t mean that the sense of responsibility we feel for that is any less,” she said.
The First Minister added: "Rightly people hold politicians like me to account for this, but please believe me when I say I carry the weight of this every single day and always will, in terms of the decisions we were taking.
“I wish I could turn the clock back.”
Ms Freeman told the BBC podcast Political Thinking with Nick Robinson last week the government had not understood the social care sector well enough.
“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,” she said.
"I think our failures were not understanding the social care sector well enough.
"So we didn't respond quickly enough to what was needed in our care homes, but also in social care in the community."
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.”