Tánaiste Simon Coveney has said he feels "sadness" as Britain leaves the European Union.
The UK will formally leave the bloc at 11.00pm Irish time on Friday.
A transition period for the UK will start on February 1st, and is set to expire at the end of December 2020.
Any agreement on the future EU-UK relationship will have to be fully concluded before that point if it is to come into force in January 2021.
Candlelit vigils are planned across Scotland, which voted to stay in the EU in the 2016 referendum.
These are aimed at sending a message to the EU to keep open a place for Scotland.
Speaking to Pat Kenny, Mr Coveney says: "My overall feeling today is one of sadness".
"A lot of my mother's family are still English and live there - I've been to university in England, I've worked in Scotland.
"In terms of the bigger picture: I think everybody loses here.
"I think Britain will lose; I think their standing in the world has been damaged and will be diminished without the solidarity that comes with EU membership.
"I think the EU will be weakened too - because Britain is a great country, it's a powerful country, it's a strong economy and it added a lot to the European Union.
"The European Union for Ireland will be quite different without the UK in it".
He says while the transition period keeps the status quo in the short-term, a lot of work still has to be done.
"Now our focus turns to the east-west relationship in terms of getting a trade deal - and a deal on whole range of other things.
"There also will need to be deals on fisheries, on energy, on transport, on aviation, on law enforcement, on data protection.
"So anybody who thinks this is a question of just agreeing 'we're starting from the same position here, so let's just keep trading with each other' - that is just nonsense."
Tánaiste @simoncoveney is in the studio now to discuss #GE2020 and #BrexitDay - join the conversation with #PKNT pic.twitter.com/e7Edx8clNU
— Pat Kenny Newstalk (@PatKennyNT) January 31, 2020
"What the UK would like to do is to turn this discussion into standards and a discussion around standards... but actually this isn't just about standards.
"If we're going to get a trade deal that doesn't have tariffs or quotas - which is really important for Ireland - the EU is going to insist on there being a level playing field between the UK and the EU in terms of how goods are produced.
"That is about standards but it's also about competition law, state aid rules and so on".
"If the UK decides that it wants to deregulate to create competitive advantage... and then expects to be able to sell those products - having gained that competitive advantage - into an EU market in a way that disadvantages EU companies, there is no way that the EU is going to facilitate that"
"I think we need to be blunt about that".
"The truth is we're losing a very powerful friend here... a country that has very similar views to Ireland on most things".
He says while Ireland is forging closer relationships with other EU member states - such as the Nordic and Baltic countries - "Ireland's going to have to work much harder in terms of building alliances and turning friendships into partnerships".
