Instead, ministers put the whole state on level 3.
This means people are asked not to leave their county except for essential reasons and are encouraged to work from home wherever possible.
One coronavirus-related death was recorded in the Republic on Thursday bringing the death toll to 1,817.
A further 506 new cases of Covid-19 were also reported.
On Monday, Mr Varadkar described the National Public Health Emergency Team (NPHET) recommendation, which would have allowed schools and crèches to remain open as “a bolt out of the blue.”
In the Dáil (lower house of parliament) on Thursday afternoon he said he was first informed of the recommendation on Sunday evening and in writing at 20:30 local time just 30 minutes before Irish broadcaster RTÉ reported what NPHET was proposing.
It should not be about the government versus NPHET, Mr Varadkar told the Dáil, adding: “This is Ireland versus the virus.”
The tánaiste repeated his criticism that moving to level 5 had “not been thought through” including the implications of the Northern Ireland dimension in the shared goal of reducing the spread of the virus.
Questioned by Sinn Féin’s Pearse Doherty, Mr Varadkar denied there was a lack of hospital capacity.
The tánaiste said the government had added 800 hospital beds – 150 of which were being used by Covid-19 patients – and there were now an additional 60 ICU beds since the spring lockdown, bringing the total to 225, with 25 being used by Covid patients.
He said the country would be able to cope if there was a surge in coronavirus cases and was in a better position to do so than some other countries whose health services “get a better press”.
NPHET officials met on Thursday to discuss their concerns about the spread of Covid-19 in the Republic of Ireland.
It said it remains deeply concerned about the rising levels, however did not recommend tightening restrictions.
Chief Medical Officer Dr Tony Holohan said the situation had deteriorated further since Sunday.
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