Ms Sturgeon made the comment at a press conference in Edinburgh today where she spoke about a "sharp rise" in cases over the last few days.
She also announced that the Scottish Government was set to launch a full public inquiry into the handling of the pandemic.
Ms Sturgeon said:
Scotland has recorded 10 coronavirus-linked deaths and 4,323 cases in the past 24 hours.
The First Minister said this takes the death toll under the daily measure - of people who first tested positive for the virus within the previous 28 days - to 8,080.
The daily test positivity rate is 14.5 per cent, up from 12.4 per cent the previous day.
A total of 364 people were in hospital on Monday with recently confirmed Covid-19, up by eight on the previous day, with 43 patients in intensive care, up two. So far, 4,850,552 people have received the first dose of a Covid-19 vaccination and 3,587,145 have had their second.
The latest daily figure of new Covid cases is the "largest we have ever recorded in a single day", Ms Sturgeon said - although she added more testing was now being carried out than in earlier stages of the pandemic.
The First Minister said: "We always knew cases were likely to rise as restrictions eased, so to some extent what we are seeing now is not entirely unexpected. That said the scale of the increase is still a cause of real concern."
With vaccination "making a big difference" Ms Sturgeon said many of the new cases were in younger people, who are "less likely" to have had both doses of vaccine.
She said that "around half of all new cases right now" were in people under the age of 25.
Ms Sturgeon also said around a third of new Covid-19 cases recently were in people who had been double dosed.
"Even with vaccination we can't be totally relaxed about this surge in cases," the First Minister said.
She warned the rise in cases in the last week "may well result in more people having to go to hospital in the coming days, perhaps requiring intensive care treatment".
Ms Sturgeon also said it was "likely" the rising cases would result in an increase in deaths.