Heath Minister Robin Swann has said it would be unfair to "point the finger" of blame at anyone following the chaotic scenes outside several hospital A&Es on Tuesday.
At one point 17 ambulances with patients were lined up outside Antrim Area Hospital, while inside 43 more patients were waiting for an emergency bed.
A further 21 were waiting at the Causeway Hospital yesterday morning.
A leading public health expert has said Mr Swann should resign over Northern Ireland's response to the pandemic.
Belfast-born Dr Gabriel Scally said that if it was up to him, he would "change the team".
The Northern Trust explained yesterday that there were no waiting ambulances outside Antrim Area Hospital, but it remained under "severe pressure".
Northern Trust chief executive Jennifer Welsh said she and her colleagues across the other four trusts were "extremely concerned" about the problems facing the health service.
She said: "You will have seen the media images of 17 ambulances parked outside Antrim Area Hospital's emergency department yesterday.
"Ambulances with sick people, doctors and nurses assessing and caring for them in the back of the ambulances because we literally had no room to bring them inside.
"That was a truly depressing spectacle and a truly grim reality, and sadly it is a scene that is played out right across the country.
"Thankfully, due to the extraordinary work by the team at Antrim and our colleagues at the Ambulance Service, the situation eased last night, but the hospital remains under severe pressure today."
Ms Welsh added the trusts have warned for months that hospitals are operating beyond capacity as waiting times for beds increase.
"It would be entirely wrong to dismiss this by saying: 'Sure, this happens every winter'," she added.
"That would be to ignore the fact that this is not a normal winter.
"Yesterday a quarter of the patients occupying beds at Antrim Hospital were Covid-positive, so that puts the growing impact of Covid-19 in perspective."
First Minister Arlene Foster expressed disappointment at the scenes.
"It's not where we want to be, and of course we always have winter pressures this time of the year, but Covid-19 has exacerbated that," she said.
Deputy First Minister Michelle O'Neill added: "It is totally unacceptable that people are being cared for in the back of ambulances, but that shows you our health service is under huge pressure, so it is very clear to me that what we need is to have an intervention, what that looks like we will discuss at the Executive tomorrow."
Meanwhile, in a tweet posted yesterday, Dr Scally, a member of the independent Sage advisory group, wrote: "The handling of Covid-19 in Northern Ireland beggars belief.
"The health service is on the brink of being overwhelmed, but efforts to prevent growth in cases have been relaxed. Shops, coffee shops, restaurants and bars serving food all open. Disaster looms."
Speaking to the Belfast Telegraph later, Dr Scally said: "If Northern Ireland was a football team playing in the Covid league they'd be in the relegation zone and the directors would be looking for a new manager and coaching staff, because the performance has been and continues to be so poor.
"The rate of deaths is dreadful and when you compare the performance to the first wave, there are very few places which have done substantially worse this time around and facing a difficult time, and Northern Ireland is one of them.
"I'm absolutely shocked about how bad it is."
Dr Scally, president of epidemiology and public health at the Royal Society of Medicine, added: "Northern Ireland had zero Covid deaths a day during the summer and case numbers were down to single figure.
"It takes monumental stupidity not to think that something has gone wrong in between and I see no effort to try and find out what can be done to put things right.
"Basically, the response in Northern Ireland is not a proper public health response. It is reactive.
"They wait for things to go wrong and then they act."
When asked if he thinks Mr Swann should resign, Dr Scally said: "I would change the team and put some public health people in there. This is a public health emergency with no public health leadership."
Ulster Unionist leader Steve Aiken said Dr Scally's "misplaced" attack was "disappointing but not surprising".
"Even when Northern Ireland had the lowest rates in the United Kingdom, Gabriel Scally was still criticising Robin Swann. Dr Scally is revelling too much in his role as chief hurler on the ditch.
"It is very easy for him to criticise from the sidelines while the Health Minister is trying to provide leadership in a five-party Executive. Gabriel Scally clearly has little understanding about how the Stormont Executive works."