Mr Ross pointed to a warning from the Scottish Chambers of Commerce that more firms will go bust in the city unless they're given greater help from the Scottish Government.
Glasgow is the only part of Scotland still under Level 3 restrictions.
The Scottish Conservative leader said Glasgow Chamber of Commerce chief executive, Stuart Patrick, had warned that 90 per cent of businesses in the city will receive less than they were promised by ministers.
Quoting the Chamber of Commerce, Mr Ross said: “The financial support offered bears no relationship to the economic damage being done by the restrictions.”
Mr Ross added that many businesses in Glasgow, which has been under lockdown restrictions for 269 days, were “struggling to survive”.
The First Minister insisted there are a “range of different support streams” in place for businesses in Glasgow, which “will remain in place for as long as is necessary”.
She added: “I know how difficult it is for residents and businesses across Glasgow but I also know how dangerous it would be if we eased restrictions too quickly and allowed a new variant of this virus, that we know is spreading perhaps even more quickly than the variant at the start of the year, to take a grip again.”
Ms Sturgeon insisted she understood the “frustration of the business community just as I understand the frustration of every single citizen across the country as we continue to grapple with a global pandemic,” but insisted that “good progress” was being made.
‘Reasons to be optimistic’
She added there were “reasons to be optimistic” about the situation in Glasgow, adding that she wanted to get the city back on track “as quickly as possible, but that’s got to be done responsibly and safely”.
She said: “We see a reduction in hospital cases today, and a small reduction in ICU cases, so there are reasons to be optimistic there, but we’ve got to continue – in the interest of business and in the interest of everybody – to take careful and cautious decisions to get the whole country back to normality.”
As part of those measures, NHS Greater Glasgow and Clyde has called on people living in the south of Glasgow aged 40 or over to visit a Covid-19 vaccination drop-in centre running at the Gurdwara in Pollokshields.
The centre is open from 11am to 6.30pm on Thursday and offers first doses or a second to those due to have it in the next eight to 12 weeks.
Two hundred appointments are available on a first come, first served basis.
While Glasgow remains in Level 3, an incident management team which was set up in Moray due to an outbreak there has now been closed with testing advice returning to normal.
Moray moved from Level 3 to Level 2 restrictions last weekend.
There have been 464 new Covid-19 cases reported in the last 24 hours, representing 1.8 per cent of all tests taken.