Taoiseach Brian Cowen has said he will be more cautious in the future about how he conducts his social life.
He said he was disappointed that the details of what had happened in Galway had come out in the media.
Mr Cowen said he had learned not to be found in a 'similar position' again and would need to leave social functions sooner.
He said it took away from the substance of the two days where a lot of important contributions had been made on the state of the economy and other issues.
The Taoiseach has said he took responsibility for what he did and said it would not happen again.
Speaking about a potential leadership challenge, Mr Cowen has said he would not get involved in speculation about a potential leadership heave within Fianna Fáil.
Mr Cowen said he had the confidence of Minister for Foreign Affairs Micheál Martin and his Cabinet, despite what happened in Galway.
He said he and his parliamentary party are committed and have a duty to continue to work on important issues such as job creation and the economy.
When asked about reports that golfer Philip Walton was insulted by Mr Cowen's impersonation of him, the Taoiseach said he counted Mr Walton as one of his great sporting heroes and he said he hoped his actions were not regarded as hurtful.
'Unfortunate incident'
Speaking on Six One News about the continuing fallout from the Taoiseach's Morning Ireland interview, Minister for Justice Dermot Ahern said it has been an unfortunate few days for Fianna Fáil.
He said the fallout has not been great for the country, but it is time to move on and deal with the issues facing the country.
Mr Ahern said Mr Cowen is up to fulfilling the Taoiseach's job, even if he did not have a good day on Tuesday and that all the Cabinet are behind him.
The minister said that backbenchers he spoke with are worried about what happened, but equally there is a clear understanding that the situation of the country is too vital for Fianna Fáil to be diverted by a party row.
He called it 'an unfortunate incident' but said they want to move on.
Asked what lessons could be learned, the minister said staying up until 3.30am before an interview is not something the Taoiseach will ever want to do again.
He said there is also a need for the party to look at think-ins.
No threat to Taoiseach - Ó Cuív
Minister for Social Protection Éamon Ó Cuív has said there was no question of the Taoiseach's position being under threat.
Mr Ó Cuív also said he did not think there would be an early General Election.
He said the Taoiseach had said he was committed to remaining in office for a full term and he had no reason to doubt that.
Mr Ó Cuív added that he had not heard of any concern within the Parliamentary Party over the events surrounding the Taoiseach's Morning Ireland interview.
He said Mr Cowen had made an apology and it was now time to move on and deal with the pressing issues the country faced, especially unemployment.
He said this was what the people wanted the Government to concentrate on.
Meanwhile, Minister Mary Hanafin has said that 'early in the morning you expect somebody at our level to be able to communicate properly and that did not happen that morning, so I can understand people being annoyed by it'.
Speaking on Highland Radio, Ms Hanafin said he sounded tired and hoarse but she added that people in New York and London were not listening to Morning Ireland.
She said that 'it was the tweet that prompted the question to the Taoiseach that forced him to deny it and it was the denial that became world news.'
The minister also said journalists were around that night and they knew he was neither hungover nor drunk.
Cowen heckled in Sligo
Meanwhile, Mr Cowen was heckled as he arrived to address a Chamber of Commerce function in Sligo tonight.
About 120 protestors had gathered at the entrance to the Clarion Hotel and shouted ‘shame, shame, shame' as the Taoiseach’s car drove in.
The protest was organised by two groups - Save Sligo Cancer Services and the Sligo Workers Alliance.
Mr Cowen, who was 40 minutes late arriving for the dinner, waved to the protesters as his car drove in but did not stop.
The protestors held up banners saying ‘The North West Wants An Apology Too’ and ‘Death By Geography’.
A number of Sinn Féin, Fine Gael, Labour and independent councillors joined the protesters.
