Two related but distinct questions are actually being asked:
- Does an question need to be set off with quotes?
- How do you deal with the internal punctuation of the interior sentence.
The answer to #1 - No, its just a single unit.
Those who say "blue" are fools.
The answer to #2 is dependent on your locale.
Per Grammar Girl's answer to the question, the closing period of "my system is foolproof" should go inside the quotes in American English, and outside (at the end of the sentence) outside of the U.S.
This your sentence should be:
Those who say "my system is foolproof!" are underestimating the ingenuity of fools.
in the U.S.
Those who say "my system is foolproof" are underestimating the ingenuity of fools.
outside the U.S.
And, by the way:
1. You can make a system fool-resistant but not fool proof.
2. You can make it fool proof, but they'll make a better fool
and 3. No one has ever lost a buck underestimating the American Public (M. Twain)