The First Minister, responding to questions following her Covid-19 update to the Scottish Parliament on Tuesday, said she did not want to repeat the mistake of opening up international travel too quickly as Scotland did last year.
Alison Johnstone, of the Scottish Greens, highlighted comments from Boris Johnson that a third wave would “wash up” on the shores of the UK.
The MSP said: “This week the Prime Minister has said that a third wave of coronavirus that has hit mainland Europe will ‘wash up' on our shores.
"I’d like to know if the First Minister shares his view, his acceptance that such an outcome is inevitable and I would like to understand what progress the Scottish Government has made in urging the UK Government to tighten border controls."
Responding, the First Minister said that importation of new cases and new variants was one of the biggest concerns for the Scottish Government.
Ms Sturgeon said: “We cannot stand and guarantee that won’t happen here.
“Washing up on our shores, it is not inevitable. One of my regrets about last year when I look back is that as we suppressed the virus so hard and successfully, we opened up international travel perhaps too quickly and too much.
"The reasons for doing that were not wrong. The industry was in dire straits and people wanted to be able to travel again, but I don’t think on reflection and in retrospect that was the right thing to do.
"I am determined we don’t do that again.
"Importation of new cases and new variants of this virus is one of the biggest risks we face.
"We have continued rules in place for managed quarantine for people coming in directly to Scotland.
"Those rules are not as restrictive in the rest of the UK and I have tried very hard to persuade the UK to emulate our policy.
"It does leave us to a greater vulnerability to importation than I would like us to have.
"I think we have got to be very, very cautious here.”