Speaking on ITV's Peston about the rise of coronavirus cases in Scotland and other parts of the UK, she said: "I think with hindsight we can say all sorts of things, maybe it would have been better if it hadn't happened.
"I know that that scheme was about trying to incentivise people to help the economy, and we can't be blind to the economic impact here."
Ms Sturgeon told ITV News Political Editor Robert Peston: "Obviously we've got university clusters just now but in recent weeks we've got two key drivers, and it's about the people coming together in people's houses, which is why in Scotland we're asking people not to visit other people's houses right now and that's really difficult, but also in hospitality settings, where people are coming together and mingling."
Pubs and restaurants in Scotland and England have to close at 10pm and the government has encouraged people to work from home if they can.
Ms Sturgeon said that the potential rise in unemployment is "extremely concerning" and "could be avoidable".
She said: "Now the replacement for the furlough scheme that the Chancellor announced last week, welcome as far as it goes, and I don't want to be churlish about that, but many commentators, many sectors say that it does not go far enough to stop a wave of redundancies that could be avoided if there was a more generous and comprehensive scheme in place."
Asked why she thinks there has been an increase in Covid-19 infections in Scotland, she said: "We suppressed the virus to lower levels in Scotland over the summer than some other parts of the UK so we started from a lower base and that increased faster and has taken us to pretty much the same level.
"But perhaps more substantively Scottish schools went back some weeks before schools in England and our universities have returned a couple of weeks ahead of universities elsewhere.
"And in universities in particular we have been quite aggressively testing students with symptoms so we’ve moved mobile testing capacity, we’ve opened up some walk-through testing centres near university campuses to try and identify as many students who are positive as possible."
She added: "But what we see is the virus rising across all parts of the UK which of course also reflects the increases that we’ve seen across Europe particularly in France and Spain in recent weeks."
Asked whether university students will be allowed to return home for Christmas or how confident she was that Scottish Highers would take place next year, she said that it was best not to give "false assurances".
"Be in no doubt, we all want students to be able to return to their family homes for Christmas," she said. "And of course for the whole population within this really difficult situation we're in just now, we hope that by Christmas we will be in a situation where families are able to come together more, but a lot of that depends of course on our success now."
She added: "We've got to contingency plan. What I can say with certainty is that we want exams to go ahead next year.
"We don't know as we go into winter just what disruption there might be to education, we're going to try very hard to avoid that, and that's why we need to do all of these other things to keep the virus under control, to keep schools open."
Also on the programme was International Trade Secretary Liz Truss who was asked for her reaction to comments made by US Presidential candidate Joe Biden's in response to the government's plan to override parts of its Brexit divorce deal.
Mr Biden said the Good Friday peace deal in Northern Ireland cannot become a “casualty” of Brexit, adding: "Any trade deal between the US and UK must be contingent upon respect for the Agreement and preventing the return of a hard border."
Ms Truss declined to say which presidential candidate she supported, adding: "We are working with both parties, both the Democrats and Republicans, who both have strong support for a trade deal with the UK and we are committed to the Good Friday Agreement.
"I will work with whoever is in the White House. It is about a strong relationship with our closest ally and friend with whom we have a lot in common."
She would not be pushed on her reaction to Donald Trump refusing to denounce white supremacy during Tuesday's first presidential debate.
She said: "We are of course committed to the equality agenda in the UK and it is not our job to interfere in foreign politics."