No, it isn't a dollar for dollar credit. It sounds like you were given a small credit and the rest is a carryover or carryback. Here is how the credit is calculated.
The IRS limits the foreign tax credit you can claim to the lesser of the amount of foreign taxes paid or the U.S. tax liability on the foreign income. The excess limit is created when the U.S. taxes on that foreign income are greater than the foreign taxes paid.
To describe more in detail, Now, you would like to know the reason why you weren't given full foreign tax credit. According to the IRS, Your foreign tax credit cannot be more than your total U.S. tax liability multiplied by a fraction. The numerator of the fraction is your taxable income from sources outside the United States. The denominator is your total taxable income from U.S. and foreign sources. Here is an example on how this works.
If your tax liability on Line 24 of your 1040 is $5000, your foreign income is $11,728, and your total income, foreign and US income, is $50,000. The foreign tax that can be claimed for this year is ($5000)($11,728/$50,000)=$1173. This is the maximum amount of credit that can be claimed this year. Any excess foreign tax credit can either be carried back to a previous year or carried forward for 10 years to offset any past or future foreign tax credit paid on foreign income. So if you had a $5000 credit, $1173 will be credited this year while $3827 will be a carryback or carryforward, or both.
Hopefully, this may give you insight way you weren't given the full amount of the credit. You might try claiming the FEIE to see which will give you a better return.
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