Taoiseach Enda Kenny has said the very clear and decisive result in the referendum was welcome, but said pledges given in Westminster for greater devolution to Scotland would have implications for the North.
Mr Kenny said he had followed the debate and the electoral process very closely. "The spirit of democracy is very much alive in Scotland. The people gave a very clear and decisive decision. What was requested was that the referendum would be fair, legal and decisive and that has been the case."
Speaking in Cork before Mr Salmond resigned, Mr Kenny said he hoped there could be real unity between both Yes and No camps.
He said it was important the institutions already set up in North, including the Northern Assembly, work as they were intended to.
“Clearly it has implications for the future. Things will not be the same in the future because the devolution of extra powers to Scotland will bring with it claims from other parts and, indeed, from other countries.”
Minister for Foreign Affairs Charlie Flanagan said there were "interesting challenges" ahead in the aftermath of the No vote.
He said there may be some changes that have implications for Ireland and other countries, but it was important to ensure positive relationships remained in place. "Our nearest neighbour is our greatest trading partner and it's our job to stay that way. Obviously there will be implications for Northern Ireland. We are awaiting an announcement by prime minister Cameron in relation to the corporation tax."
Fianna Fáil leader Micheál Martin said the Belfast Agreement included the involvement of the Irish Government in any changes to the status of Northern Ireland.
“At the core of the Good Friday agreement is an international treaty between the British and Irish governments.
“I am calling on the Taoiseach to immediately make a statement confirming that the Irish Government will be a full participant in discussions about changes to the status and powers of the Northern Assembly and Executive.”