The First Minister insisted the "buck stops" with her but noted it is a matter of public record that Mr Mackay was transport minister at the time the contract was signed.
It comes after further delays were announced to the completion of the two vessels at the centre of the controversy, Glen Sannox and Hull 802.
They will not enter service until next year at the earliest, with their cost rising to around £240 million - two and half times the original price.
In a damning report, public spending watchdog Audit Scotland called into question ministers' decision to award the contract to Ferguson Marine despite the "severe misgivings" of experts because of the yard's inability to provide mandatory financial guarantees.
Finance Secretary Kate Forbes updated Holyrood on Wednesday, laying out the further cost overrun and delay, which she said was due to an issue with cabling that was purchased before the Scottish Government saved the yard from closure in 2019.
However, she was unable to say who decided to proceed with the contract.
Speaking at First Minister's Questions, Scottish Conservative leader Douglas Ross asked for a "straight answer" on which minister gave the "green light".
Ms Sturgeon said: "Who was transport minister at the time in question is of course a matter of public record. That was Derek Mackay.
"But of course, this is a government - and this may be alien to the Conservatives, I understand - but this is a government that operates by collective responsibility.
"And ultimately, as with any decisions, whether I am personally involved in them or not, responsibility stops with me."
Mr Mackay quit Holyrood in February 2020 after it emerged he had bombarded a 16-year-old boy with messages.
Mr Ross told the First Minister it is “very convenient that the person getting the blame is no longer here”.
Ms Sturgeon rejected the accusation that she was throwing Mr Mackay “under the bus”, and said: “This is a government that operates by collective responsibility and I am responsible, ultimately, for all of the decisions that the government takes – the buck stops with me."
She continued: “I am not defending the cost overruns, the delay around the construction of these ferries – it is completely unacceptable.
“But at all points, the motivation of this Government has been to save jobs, save the shipyard and make sure that these ferries – albeit late and that is a matter of deep regret – can be delivered, and that is what we continue to focus on.”
Mr Ross repeated his calls for a public inquiry and referenced a passage in the Audit Scotland report which said: “There is no documented evidence to confirm why Scottish ministers were willing to accept the risks of awarding the contract to (Ferguson Marine), despite (Caledonian Maritime Assets Limited’s) concerns.”
He said it was “one of the most reckless decisions ever taken by a Scottish Government” and “one of the worst public spending disasters since devolution”.
Ms Sturgeon pointed to a recommendation in the report which calls for a “review” to be undertaken when the vessels are complete, insisting ministers will “consider what form that further review will take”.