The Prime Minister fielded calls for an extension of the jobs furlough scheme during an emergency Cobra meeting with devolved ministers.
The British Government was not forthcoming with support in response, Northern Ireland’s deputy First Minister Michelle O’Neill said.
A so-called circuit breaker, a short-term return to lockdown, was not discussed during the virtual meeting with Boris Johnson, the Sinn Fein vice-president added.
She said: “It is very clear that we all need to take action that is commensurate to the risk posed in each of our areas of responsibility.
“I made it very clear in the conversation today that we need to have a very focused north-south, east-west approach, that we need to be working across this island and between the two islands in terms of our response.
“We are facing a very difficult winter. I raised the issue of the furlough scheme and financial supports if we have to take more draconian measures, which I hope that we do not get to that point.”
On Thursday, Stormont ministers will discuss what potential “tools” they can use to handle the current stage of the crisis.
There were 75 new confirmed cases of Covid-19 in Northern Ireland reported on Tuesday.
There were no further deaths recorded by the Department of Health. The death toll recorded by the department remained at 577.
Ms O’Neill added: “It was necessary to raise those issues because ultimately when you have to move draconian measures then we need to be able to financially support families and workers and be able to allow them to do the right thing in what is going to be a very difficult winter.”
Fresh Covid-19 restrictions were extended to all of Northern Ireland on Tuesday evening.
There can be no mixing of households indoors, with some exemptions, while no more than six people from two households can meet in a garden.
Previously, the measures only applied to Belfast and Ballymena in Co Antrim.
The deputy First Minister said: “I also want to prioritise schools remaining open.
“We have an inevitable rise in positive cases, that is going to continue but the window of opportunity should not be missed. We have a chance now in the next two to three weeks to try and reverse the trend.”
She said they had to consider whether lessons could be learned from how people had responded globally.
Pubs which do not serve food are due to open on Wednesday, despite the fresh restrictions.
Ms O’Neill said: “I think it is a confusing message that you are moving towards opening up a sector, but the pub sector is the only part of that entire hospitality sector that has not opened.
“You have to be reasonable about that, 30,000 jobs are impacted by that sector not being opened.”
She said there was a difference between a regulated setting with good hygiene measures in place and people’s own homes, where they feel more relaxed and are less likely to wash their hands.
“I accept that is a slightly conflicting message there but we would only be moving forward if the science and health advice say that we can,” she added.
First Minister Arlene Foster also reiterated her call for the Government to extend the furlough scheme beyond October.
“It is incumbent upon us all to recognise that financially we cannot expect to take action which impacts upon people and then not give them the assistance they need,” she said.
The DUP leader stressed the need for a common approach across the UK.
Challenged on the rationale for allowing the reopening of so-called wet pubs to proceed, Mrs Foster insisted recent infection clusters were not associated with hospitality sector businesses that have been open since the summer.
She said a two-week period of lockdown to try to halt the spread of the virus could not be ruled out.
The First Minister said if people adhered to the new restrictions, more severe steps could be avoided.
She added: “What we’re trying to say to people is please work with us now in relation to these limited restrictions and, if you do that, then we may hope not to have to get into a situation where we have to take other graduated steps.
“Of course, the circuit breaker will be towards the end of those steps, because it would be a lockdown affecting the whole of society.”