The 73-year-old Italian held talks with Football Association of Ireland chief executive John Delaney on Friday to discuss matters raised at Wednesday night's Board meeting, at which Trapattoni was given the association's continued backing following a difficult few days.
The meeting between the pair at the FAI's Abbotstown headquarters was described as "workmanlike and professional" by a spokesman, and the manager later confirmed his satisfaction with what was said.
Trapattoni said: "John and I met today to clarify the thoughts of the board and these were agreed and confirmed by me.
"It was a useful and professional conversation and I thank him for this.
"During the meeting, we discussed a number points that were raised by the board to help us continue to improve our work for the association."
Trapattoni headed for the Faroe Islands at the weekend with his job in severe jeopardy after Friday night's 6-1 World Cup qualifying defeat by Germany at the Aviva Stadium.
Despite one source suggesting that he would be out of work by the end of the week whatever happened in Torshavn, he returned with a 4-1 victory and, hours after he touched down in Dublin, to a public expression of the FA board's continued support.
However, the issues which provided the fuel for his critics as the pressure mounted - his conservative approach, his tactical inflexibility an his communication with players, to name but three - remain to be addressed.
Whether or not they were on the agenda as he met Delaney will remain private, but his employers will be looking for evidence of improvement when the Republic return to competitive action against Sweden and Austria in March next year, two games which could have a major say in their hopes of making it to Brazil in 2014, and Trapattoni's long-term future.