The Collaborative International Dictionary of English v.0.48:

Inexcusably \In`ex*cus"a*bly\, adv.
   With a degree of guilt or folly beyond excuse or
   justification.
   [1913 Webster]

         Inexcusably obstinate and perverse.      --Jortin.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inexcusably
    adv 1: in an unpardonable manner or to an unpardonable degree;
           "he was inexcusably cruel to his wife" [syn:
           inexcusably, unpardonably, unforgivably] [ant:
           excusably, forgivably, pardonably]
    2: without any excuse; "he is unjustifiably harsh on her" [syn:
       unjustifiably, inexcusably] [ant: justifiably]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "inexcusably":
   abominably, agonizingly, awfully, baldly, balefully, bitterly,
   blatantly, brashly, confoundedly, cruelly, damnably, deadly,
   deathly, deucedly, distressingly, dolorously, dreadfully,
   egregiously, excessively, excruciatingly, exorbitantly,
   extravagantly, flagrantly, frightfully, grievously, hellishly,
   horribly, improperly, indefensibly, inexpiably, infernally,
   iniquitously, inordinately, interestedly, intolerably,
   irremissibly, lamentably, miserably, nakedly, one-sidedly, openly,
   painfully, partially, piteously, sadly, shatteringly, shockingly,
   something awful, something fierce, sorely, staggeringly, terribly,
   torturously, unallowably, unashamedly, unbearably, unconscionably,
   undeservedly, undispassionately, unduly, unequally, unevenly,
   unfairly, unforgivably, unjustifiably, unjustly, unpardonably,
   unreasonably, unwarrantably, woefully, wrongfully, wrongly