sensibility
Pronunciation:
/ˌsɛnsɪˈbɪlɪti/noun
Definitions
The ability to sense, feel or perceive; responsiveness to sensory stimuli; sensitivity.
Emotional or artistic awareness; keen sensitivity to matters of feeling or creative expression.
Excessive emotional awareness; the fact or quality of being overemotional.
(in the plural) An acute awareness or feeling.
Example: I apologize if I offended your sensibilities, but that's the truth of the matter.