Earlier this week, Mrs May rejected Europe's draft withdrawal agreement
The Taoiseach Leo Varadkar said he 'remains concerned' the constraints of leaving the EU Customs Union are still not fully recognised by Britain.
He made the comments after a key speech by British Prime Minister Theresa May over the UK's future relationship with the bloc.
Speaking in London earlier, Mrs May stood firm in calling for a different relationship than Canada, Norway and Turkey have with the EU, declaring: "If this is cherry picking, then every trade agreement is cherry picking."
She repeated a "hard fact" that Britain would leave the EU customs union and single market.
"Life is going to be different," she said. "In certain ways, our right to each other's markets is going to be different to what it is now."
But Mrs May called for "reciprocal binding commitments" on some policy areas and voiced hopes Britain would still stay signed up to a number of EU agencies.
That includes the European Medicines Agency, which is relocating its headquarters from London to Amsterdam because of Brexit.
Mrs May also claimed negotiators were "close to an agreement" on the terms of an implementation period, despite Mr Barnier warning this week that it was still not a given.
And she struck a conciliatory tone by saying neither side would get "exactly what we want" from the talks, and signalling Britain would not fight losing EU passporting rights.
On the contentious issue of the European Court of Justice (ECJ), Mrs May said its jurisdiction in Britain "must end".
She called for a third party court to be set up that would resolve trade disputes, instead.
Despite her efforts to quell fears of a hard Irish border, she accidentally began a sentence: "To achieve a hard border-."
She then corrected herself: "To avoid a hard border…"
Mrs May backed "new technology" to help keep the border between Northern Ireland and the Republic as 'soft' as possible.
The speech was well received by her confidence and supply partners the DUP, with the party's leader Arlene Foster "particularly welcoming" a commitment to "strengthen" the UK union.
Responding to the speech, Mr Varadkar said: "I have listened to the Prime Minister’s speech, and the Government will study it closely.
"She has given a number of important reassurances today, which I welcome, including restating her overall goal of a very close relationship with the EU.
"I particularly welcome her clear commitment to the Good Friday Agreement, the Northern Ireland peace process and the need to avoid a hard border, and to the agreement reached between the UK and the EU in their December Joint Report.
"The speech included a number of signals about the type of future economic relationship that the UK Government wants. But it also recognised that the UK will face hard choices given constraints between some of the UK aims and the consequences of withdrawing from the European Union.
"For our part, a close economic relationship is very much in the interests of Irish business, as is a smooth transition period.
"However, I remain concerned that some of the constraints of leaving the Customs Union and the Single Market are still not fully recognised.
"We will now need to see more detailed and realistic proposals from the UK. Brexit is due to happen in a little over 12 months, so time is short."
He added that: "Progress on the Withdrawal Agreement published last week will be important in the context of that next phase of work."
Tánaiste Simon Coveney said: "We welcome the Prime Minister's reiteration of the UK's steadfast commitment to the Good Friday Agreement and to the commitments made in the agreement reached last December, including on avoiding a hard border.
"These commitments now need to be translated into concrete proposals on how a hard border can be avoided and the Good Friday Agreement and North-South co-operation protected."
"The draft Withdrawal Agreement text published by the Task Force this week outlines the fall-back mechanism, as agreed in December, if the first two options cannot meet our objectives.
"This would entail, if necessary, full alignment in Northern Ireland with those rules of the Single Market and Customs Union necessary to protect North-South cooperation, the all-island economy and the Good Friday Agreement, and to avoid a hard border.
"All of these options are consistent with the need to respect the provisions of the Good Friday Agreement regarding the constitutional status of Northern Ireland and the principle of consent.”
The EU's chief negotiator also "welcomed" Mrs May's words.
Michel Barnier said: "Clarity about the UK leaving the single market and customs union and recognition of trade-offs will inform EU Council guidelines re: a future free trade agreement."