Her comments come as Scottish Tory leader Douglas Ross called for the SNP’s “anti-business approach” to end.
The party said more than 50 businesses have already supported their call for restrictions to be safely eased at a faster pace, lifting lockdown restrictions three weeks ahead of the SNP’s schedule.
The Scottish Conservatives have said venues should be able to serve alcohol indoors and other restrictions due to be lifted on May 17 should have been lifted today, with the exception of rules on indoor mixing.
Hospitality groups have warned current restrictions mean many businesses will remain closed and they will continue struggling to earn a living.
The comments come as former Scottish justice secretary Kenny MacAskill’s calls to cut duty in pubs and raise it in off-sales were supported by the Scottish Licensed Trade Association (SLTA).
Mr MacAskill, MP for East Lothian and a candidate for Alex Salmond’s Alba party, has suggested that reducing alcohol duty would boost hard-pressed licensees who are not able to fully reopen their pubs and bars in Scotland until May 17 and even then businesses would still be under strict coronavirus restrictions.
Paul Waterson, spokesman for the SLTA, said: “We agree with Mr MacAskill that to help sustain pubs and at the same time reduce harmful drinking, an increase in the level of duty charged on off-sales would allow for a reduction of the duty imposed in supermarkets and off-sales."
Mr Ross pointed to the UK-wide wholesale review of duty, which is being undertaken by the Treasury.
He said: “The Conservative manifesto for the UK election in 2019 committed to a review on duty, particularly because whisky is taxed more heavily than other forms of alcohol. I think it's right that we look at this in the round, and look at all the industries that are dependent upon this.”
He said of the call for pubs’ duty to be cut: “If that is further work that needs to be done.”
Speaking as cafes, restaurants and bars opened for indoor dining without alcohol and outdoor alcoholic drinks, today, Mr Ross said: “It’s fantastic to see businesses finally start to reopen after the incredibly difficult year they’ve battled through.
"The success of Scotland and the UK’s vaccine scheme means we can afford to safely speed up the easing of restrictions, and dozens of businesses have backed our calls to bring forward those reopening dates.”
Ms Sturgeon disagreed with Mr Ross's calls for restrictions to be lifted faster.
"I, every single day, worry about the impact of all of this on business and there's a lot of focus on immediate support to business in terms of Covid recovery,” he said.
"But I also know if we open up too quickly, we run the risk of the virus running out of control again and taking not just the economy backwards, but resulting in a greater loss of life and I'm not prepared to play fast and loose when human health and lives are on the line.
"It's not about being anti-business at all, but being careful and cautious and leading the country through this pandemic.”