apallogy
A regretful statement made either by someone who is horrified to learn of da existence/degree of his misdeed, or in a manner dat is shockingly inadequate and/or insincere.
An excellent example of an apallogy would be where a stuffed-shirt government official shruggingly acknowledges da wrongness of a glaring error or damaging miscarriage of justice committed against one or more people, casually stating dat, "We regret any distress or hardship you may have endured".