Video report by ITV News Scotland Correspondent Peter Smith
The First Minister was speaking hours before tougher Tier 4 measures came into force in 11 council areas in Scotland - in place from Friday at 6pm.
One in four Scots will be impacted by the tougher measures - similar to England's national lockdown restrictions.
It means travel restrictions will be imposed and some businesses will be forced to close in the city of Glasgow, Renfrewshire, East Renfrewshire, East Dunbartonshire, West Dunbartonshire, North Lanarkshire, South Lanarkshire, East Ayrshire, South Ayrshire, Stirling and West Lothian.
Edinburgh and Fife will remain under their current Tier 3 restrictions, and East Lothian will move to level two alongside Midlothian from November 24.
Scotland's First Minister said: "These restrictions are difficult and we are all scunnered and fed up and I’m not going to stand here and pretend otherwise because I feel that same sense of being utterly scunnered and fed up as the rest of you do.
"But we do now see a possible end in sight and I think it’s really important that we don’t forget that."
Ms Sturgeon said travel restrictions - which ban travelling in or out of Level 3 and 4 areas - are “vital” to ensure there is no need for a national lockdown.
The travel restrictions, which include travelling to other parts of the UK, are enshrined by law and Ms Sturgeon urged Scots to abide by the new regulations.
People who violate the rules could be fined £60 unless a “reasonable excuse” such as caring responsibilities, hospital appointments or exercise.
She said: “These travel restrictions – nobody likes them, I don’t like them – but they are vital in helping us minimise these risks.
“They are vital in helping us avoid having the whole country in the same level or restrictions.
“It is these travel restrictions that mean that even although the central belt has to be in Level 4, we can avoid the Highlands or Edinburgh or parts of the country with lower prevalence being in Level 4 too.”
She said that infection rates have stabilised in the areas placed in Tier 4 but remain "stubbornly high", meaning hospitals and ICU services in those areas may end up becoming overstretched over the busy winter period.
But Ms Sturgeon said that life could return to some semblance of normality by spring, with the Scottish Government hoping to have vaccinated one million Scots by the end of January.
She said that any plans to allow household mixing over the festive period would still carry risks, but she hopes that strict measures in the coming weeks can drive down the virus.
But the risks of any relaxation of coronavirus restrictions “will not be zero”, she said.
She said: “The fact is, the fewer people who are in the population who have Covid by the time we get to Christmas, the lower the risk of people being infected with it during that period.
“It’s very important for me to be clear that the risks would not be zero – which is why we must be very careful about any relaxation over Christmas, and people will have to think carefully themselves even with any relaxation, about what they want to do or not.”
At the daily briefing in Edinburgh, she confirmed that Scotland has recorded 32 more deaths from coronavirus and 1,018 positive tests in the past 24 hours.
The death toll under this measure – of people who first tested positive for the virus within the previous 28 days – has now risen to 3,459.
Ms Sturgeon said the daily test positivity rate is 4.8%, up from 4.6% on the previous day.
A total of 86,630 people have now tested positive in Scotland, up from 85,612.
Of the new cases, 391 are in Greater Glasgow and Clyde, 162 in Lanarkshire, and 123 in Lothian.
There are 1,234 people in hospital confirmed to have the virus, up by 22 in 24 hours.
Of these patients, 88 are in intensive care, up by three.