Sinn Féin President Mary Lou McDonald said Brexiteers had to accept that new trading borders between Great Britain and the island of Ireland were a permanent consequence of the UK's exit from the EU.
Ms McDonald said the focus now needed to be on resolving initial problems with new Irish Sea trading arrangements, not ditching the Northern Ireland Protocol that now governs the movement of goods.
"Brexit is for keeps, I mean this is a big game changer for all of us and it has to be managed in a way that is sensible, in a way that is fair," she told Sky News.
"None of us wanted trading barriers between our island and the island to Britain, or across the continent, but Brexit has happened and in some respects those that advocated it so strongly now need to very much accept the fact that these are the consequences of their decisions.
Foreign affairs minister Simon Coveney has said the Irish Government is open to "modest extensions" of grace periods associated with the Northern Ireland Protocol.
However, Mr Coveney insisted there could be no renegotiation of the terms of the protocol, which governs trade between GB and NI post-Brexit.
"We need to try to find accommodation for each other here that can reduce tensions in Northern Ireland, can respond to legitimate concerns, regardless of who's raising them, so that we can show that the protocol can be flexible when needed," he told RTÉ Radio One.
"But at the same time that is not a renegotiation of the protocol, it's about using the protocol as it is now and flexibilities within it. And certainly I would be open to advocating for modest extensions of grace periods when appropriate to try to, first of all, reassure people that we're listening to them in Northern Ireland, because we are, and then, secondly, so that we can ensure that businesses can operate as best they can under the protocol.
"But that's not the same thing as scrapping the protocol and it's important to make a strong distinction between the two."
Simon Coveney insisted the protocol was generally working, highlighting that the volume of goods arriving into Northern Ireland ports was similar to this time last year.
Responding to a claim from Arlene Foster that he was "tone deaf" to unionist concerns about the protocol, Mr Coveney insisted he was just trying to be honest.
"Calls to scrap the protocol because there are some issues in terms of implementation just isn't realistic and I've tried to be as honest about that as I can this week," he said.
"That does not mean trying to pick a fight with the DUP, it's just me being honest with people.
SDLP leader Colum Eastwood has warned that powersharing in Northern Ireland could be under threat if political unionism continues to agitate for the "unrealistic" scrapping of new Irish Sea trading arrangements.
Mr Eastwood urged the DUP to end talk of political boycotts and dial down the rhetoric, and instead join with other Stormont parties to find workable solutions to issues linked to the Northern Ireland Protocol.
Asked by RTÉ if there could be a threat to powersharing if unionists took an increasingly hardline approach to the protocol, Mr Eastwood said: "Yes, I think there could be and unionism needs to learn the lesson that they should have learned a number of times over the past 100 years - the British Government will let you down and if you keep going to the right you're going to end up in a worse position when you come back to the table.
"So come and work with us, let's get together, the spirit of powersharing is what's important right now, working in partnership to deal with the problems.
"But continuing to run to the microphone, have petitions and talk about protests and all that - none of that works, it's not based in reality.
"We know the DUP campaigned for Brexit, it was a strategic error at the time.
"We can now work together to resolve some of the difficulty, but let's all calm down, work together, put the rhetoric at the door because it's not going to help and it will have a political impact.
"We're seeing stability being rocked this week in a number of different ways and I think as political leaders we all have a responsibility, first and foremost, to be honest with our people and tell them what the scenario is, what the context is, why we have trading barriers and also come together to work through it, because the alternative is just not worth contemplating."