Her comments came after the National Records of Scotland also published figures on Wednesday showing that nearly 8,000 Scottish deaths have been linked to coronavirus since the start of the pandemic.
Speaking at her daily briefing, Ms Sturgeon held a moment’s silence for the 7,902 Scots who have so far died.
“That number... is a difficult one for any of us to grasp and to properly comprehend,” she said.
“And, of course, yesterday the death toll across the UK as a whole passed 100,000.
“Those numbers should make anyone in a position of authority - and I know they certainly make me - think very hard about what more we could have done and what lessons we must continue to learn.
“I know that I, and everyone in my government have tried every day to do everything we possibly can.
“But I don't think any of us, reflecting on numbers like these, can conclude that we have always succeeded.
“And for any mistakes we have made, personally I take responsibility for that.
“I am, and I always will be, truly sorry for any mistakes we have made,” Ms Sturgeon added.
“None of the people who have died are statistics. They are human beings who are lost and who right now are being mourned by friends and families.
“We should never ever forget that.”
Addressing Scots who have lost loved ones to the virus directly, Ms Sturgeon said: “I do want you to know that your loss weighs heavily on me and it always will.”
NRS data published on Wednesday showed that there have been 448 coronavirus deaths in Scotland in the last week – the highest number since last May.
It marks an increase of 75 on the previous week’s fatalities.
The majority of deaths occurred in hospitals (294), while there were 111 in care homes, 35 at home or in non-institutional settings, and eight in other institutions.
At council level, the highest number of deaths over the past week occurred in North Lanarkshire (48), followed by Glasgow city (43) and Fife (33).