If you did not break residence in Ireland, you would have remained taxable in Ireland on your worldwide income for the year.
Under the Double Tax Treaty, there is provision for claiming a credit in Ireland for the US tax paid.
This means that you are not doubly taxed.
If you did not get a credit for your US tax paid, you should have this reviewed by the Revenue.
However, if you did actually break Irish residence you should have calimed split year relief, and therefore not been taxed in Ireland on your US income in the year you left Ireland.
You should really take professional advice if you can't resolve this issue yourself.