A vote on the future of Northern Ireland's border is not necessary following Scotland's 'No' vote, First Minister Peter Robinson has said.
The DUP leader said: "More and more people in Northern Ireland want to maintain the status quo."
Sinn Féin Deputy First Minister Martin McGuinness said the United Kingdom would "never be the same again".
He said a similar debate to the "exciting and enthralling" one in Scotland was possible.
"I think we could do the same here, and we can do it without opening up divisions that would be detrimental to the institutions which we are part of at the moment," he said.
However, Mr Robinson said: "The law requires the secretary of state to be convinced there is the possibility of change - every opinion poll is going in the opposite direction."
He added: "I don't run away from any ballot that allows the people of Northern Ireland to determine what's best for them - I have no doubt what the outcome would be."
Mr McGuinness said "things have changed utterly", and Stormont politicians "need to have a united voice in entering into future discussions" on taxation and government spending.
"What we need to do is find a large measure of agreement on what extra powers we think can benefit the people that we represent, including fiscal powers," he said.
Mr McGuinness added: "From our perspective, we would want to enter that debate, recognising that there will be in all probability a commonality of approach between the Scots, the Welsh and ourselves.
"Our job here is that we have to have a united approach - can we get that? I think it is absolutely achievable."
However, Mr Robinson said: "I would always be more impressed when people ask for the transfer of full fiscal powers if they had shown a competence in dealing with the powers that we have.
"There is no point in giving to an executive more powers to manage their finances if they are not capable of taking difficult decisions with the powers they have."
The issue of implementing welfare reform in Northern Ireland has divided the parties in recent months.
Mr McGuinness said: "I'm not fighting with Peter Robinson and the DUP over welfare cuts - my argument is with David Cameron and the decision that his government took to bring that hammer blow down on us after we negotiated a programme for government."
Mr Robinson said the pledges made by the three Westminster party leaders in the days before the referendum would not change the issue.
"What is likely to be the limit of anything that would happen in Scotland in the issue of welfare reform is that they would have the same power as we have and the same ability that we have to top up any arrangements that have been agreed at a UK level," he said.
"That means that you have to find the money yourself.
"I'm happy to look at powers but that has to go alongside a mechanism to deal with those powers in an effective and efficient manner.
"If you have those kind of powers, you can't have deadlock in your executive."
Mr Robinson discussed the implications of the Scottish vote with his Welsh counterpart Carwyn Jones on Friday
Prime Minister David Cameron said he was "delighted" by the outcome of the vote, and the UK must now work to ensure Northern Ireland's devolved institutions function effectively.
"Just as Scotland will vote separately in the Scottish parliament on their issues of tax, spending and welfare, so too England, as well as Wales and Northern Ireland, should be able to vote on these issues and all this must take place in tandem with and at the same pace as the settlement for Scotland."
BBC Radio Ulster's Talkback and Evening Extra will be live from Scotland on Friday.
BBC Newsline's Tara Mills will be joined in Edinburgh by BBC NI's political correspondent Gareth Gordon to report on the reaction in Scotland to the referendum result on Newsline at 13:30 BST and 18:30 BST on Friday.