Ignoring the EU referendum result would be a "grave mistake", a DUP MLA has warned.
Prominent Leave campaigner Christopher Stalford also dismissed as "crazy" some of the proposals to block Brexit.
He said: "The reality is that the people of this country were offered a choice and they made their choice.
"Had the vote gone the other way I would have had to take it on the chin and move on.
"Over the last 48 hours we have heard all sorts of crazy and interesting ideas as to how the people's verdict can be overturned. I say to go down that road and to ignore the democratic verdict of people of this United Kingdom would be a grave mistake."
The fractious debate was the first item on the agenda at Stormont after Opposition leader Mike Nesbitt tabled an emergency motion for discussion.
At times, Speaker Robin Newton had to issue warnings for MLAs to listen with respect.
In Northern Ireland 56% of voters backed remain while 44% said they wanted to leave the European Union.
While, the Ulster Unionist Party (UUP) accepted the outcome Mr Nesbitt claimed the country had been plunged into a period of uncertainty and there were big questions for the region's political leaders.
"The result is the result - there is no point in trying to say it was a non-binding referendum, that Parliament is sovereign," he said.
"We are on our way out. We have to accept that but we have to acknowledge that within Northern Ireland 56% of people who voted, voted to remain."
Of the five main parties at Stormont, just the Democratic Unionists backed Brexit.
Mr Nesbitt questioned how First Minister Arlene Foster would balance her party political views against the region's wishes adding that there would be huge and unintended consequences for Northern Ireland.
"It is not just about the peace funds, and we all agree we have done well from peace funds," he added.
"But it is about the competitive draw down; it is about the common agricultural policy; the single farm payment; it is about our universities; our community and voluntary sector, it is about infrastructure - can we even compete for infrastructure funds?
"What about corporation tax? What happens now? Is there an opportunity to get it without a hit to the block grant or has it gone for good? This is the sort of clarity that we seek."
Sinn Fein's Conor Murphy said people in his border constituency were "fearful and bewildered" about their future.
But the veteran republican called for politicians on all sides to "row in" behind the Executive to work with the Irish, Scottish and European "friends" to find the best deal possible.
He said: "We have a responsibility collectively, in the absence of any direction from London, to chart the best course for the people that we represent and to give clarity."
In an impassioned speech, SDLP leader Colum Eastwood vowed to fight against being "dragged out of the EU by the right wing of the Tory party".
He said: "People in Northern Ireland told us that they wanted to remain within the European Union and we are going to look for every single device possible to make sure that happens and I hope others join with us."
While the Brexit vote has triggered a renewed debate on Irish unity with Sinn Fein calls for a border poll, Mr Eastwood said the time was not right for such a move.
"I believe we should have a border poll that we could actually win," he added.
Meanwhile, Naomi Long, deputy leader of the cross community Alliance Party, described the referendum result as regrettable but said it must be accepted.
She said: "To do otherwise would leave an electorate which was already angry and disaffected more angry and disaffected.
"No government should ever go to the people and ask their view on a matter simply to ignore the view that they are given by the people."
However, Ms Long said it would be appropriate for any future government to ask whether the electorate was happy with the new arrangements.
She also called for recognition of the sharp divide that has opened up between the UK nations which voted to remain and those that backed Brexit.
"To ignore that, to fail to seek an accommodation of those views is I believe to place the future of the United Kingdom in peril," she warned.
