There are situations when, if you fail to take the Foreign Earned Income Exclusion, and the IRS assesses tax, you cannot then take the FEIE to avoid that tax. Those situations are described on page 20 ("When You Can Choose the Exclusion") of
IRS Publication 54 (2014 edition at least).
To summarize, if you've failed to take the Foreign Earned Income Exclusion in timely fashion (as defined in that publication), and if you owe income tax (whether paid or not) after taking into account the FEIE (for example, on U.S. source income or on non-excluded income), and if the IRS discovers that you failed to choose the exclusion (they have done that, it would appear), you cannot then take the FEIE -- it's too late. That's a lot of ifs, but if I've just described your situation the IRS will be able to sustain its tax assessment.
If I've just described your situation you can ask the IRS for relief -- for example by making an
Offer in Compromise if there would be a genuine hardship in paying the tax you owe.
On edit: I should add that the Foreign Tax Credit (IRS Form 1116) is still available on that income even if the above circumstances describe your situation, and assuming you paid some amount of foreign income tax on that income.