The country could find itself grappling with another worrying spread of coronavirus soon if daily cases start to rise again and the R number also increases.
The warning was sounded by chief medical officer Dr Tony Holohan yesterday and comes as a signal that the National Public Health Emergency Team (Nphet), which meets tomorrow to make recommendations for reopening the country after lockdown, will take a guarded approach.
He said the drop in cases to 252 yesterday and no new deaths was "one day's data".
Numbers are likely to increase today and tomorrow because of the weekend effect, which tends to see a lower number of positive tests reported on Mondays.
"The five-day average is still over 300 cases a day. That is significant level of infections," Dr Holohan said.
If the R number - the number of people each person with Covid-19 infects - went slightly above one, in combination with 300 cases a day, there would be "problems for us in a relatively short period of time."
Earlier, he referred to data showing people are getting more relaxed about the pandemic.
One in three of us now believes the worst is behind us and our worry levels are at the same as in July, when many of us were on staycations and sceptical about a second wave
Fewer people are also staying at home, signalling relatively small but significant changes, said Dr Holohan.
He acknowledged it was natural that if people regarded the situation as improving that they would relax their guard.
That could be linked to the optimistic news around potential new Covid-19 vaccines.
"It's perfectly reasonable that people have hope around vaccines and we have hope ourselves in relation to vaccines."
However, he stressed the vaccine will not be available in the coming weeks to interrupt the spread of the virus, so we have to "stick to basic rules to help us get through the weeks ahead".
He would not be drawn on what recommendations will be made tomorrow but he has previously referred to a "lost" week in lockdown, where cases failed to drop.
Ireland is doing better compared to our European neighbours and now has a 14-day incidence rate of 108.7 per 100,000. Only Finland is better at 70 per 100,000.
Yesterday's new cases included 88 in Dublin, 26 in Cork, 21 in Kilkenny, 16 in Louth, 16 in Mayo.
The other 85 were spread across another 20 counties .
There were 289 patients with Covid-19 in hospitals yesterday, including 33 in intensive care
Asked about reported celebrations around the GAA championship matches at the weekend, Dr Holohan said "teams that win tight matches tend to celebrate" and added we have tipped too much into blame and the "nearest lamp post to hang that person from".
We have to have tolerance when there is a high level of behaviour expected of people, he added.