The amount of credit you get for foreign tax paid depends on the what the Revenue call your Effective Irish Tax Rate
If the percentage tax deducted by the foreign authority is higher than your Effective Irish Tax Rate, then the amount allowed as a Tax credit is limited to the Effective Irish Tax Rate
For example, suppose your Effective Irish Tax Rate is 10% and the US deducted 15%
Gross income 100
US tax 15
Net Income 85
The Revenue will re-calculate the gross income using the formula 85 / (100% - 10%) to get 94.44 rather than the 100
The tax credit is now 94.44 x 10% = 9.44 and not 15
Your Effective Irish Tax Rate is calculated based on the tax due on your total income, Irish and Foreign, using your normal tax credits and ignoring any foreign tax paid