The comments come after the BBC reported allegations from former Number 10 adviser Dominic Cummings that the Prime Minister resisted calls for a lockdown in the autumn of 2020 due to the fact most deaths were in the over 80 age range.
Responding to a question by Sky News at a Covid-19 briefing, the First Minister said she did not know the veracity of the claims and that it would not be appropriate to “comment in detail”.
However, the SNP leader went on to say that while there is a “heavy responsibility” on the shoulders of leaders, it is unacceptable for anyone to be “glib or complacent” about human life.
She said: “I don't know what Boris Johnson said or didn't say in relation to the allegations from Dominic Cummings, so it's probably not appropriate for me to really comment in detail on that – other than to say two things I suppose.
"Firstly, nobody, and certainly nobody in a position like mine or Boris Johnson's, should be glib or complacent about human life, whether that's the human life of a child, a young adult or an older adult.
"Human life is human life, and as decision-makers, I think it has been a heavy responsibility on all of our shoulders to try to take decisions that we recognise cannot save every person from this virus, but that minimises the impact of it, taking account of the restrictions that are in place as well, but to minimise the human impact of this.
"I think any leader who doesn't take that seriously should be asking themselves questions about whether they are fit for office.
"But I don't know what Boris Johnson's comment there were, so I'm not going to go further."
In an interview with the BBC, the former aide Mr Cummings claimed the Conservative leader had wanted to let Covid-19 “wash through the country” rather than destroying the economy because he believed those dying from it were “essentially all over 80”.
He claimed that Mr Johnson “always referred” to the Daily Telegraph for guidance, allegedly describing it as “my real boss”.
Mr Cummings, who quit earlier this year and was defended by ministers last year after breaching Covid-19 restrictions to drive from London to Barnard Castle, added that Mr Johnson responded with “no, no no, no, no, I'm not doing it” when pushed to implement stricter restrictions in September.
Commenting on the credibility of Mr Cummings, the First Minister said she had been a critic of the former aide in the past, stating: “I'm not going to suddenly now decide that he speaks gospel on everything.
"I would be a bit sceptical about some of what he is saying."
However, she added the Prime Minister “appeared to be reluctant” when it came to imposing restrictions in the autumn.