The Collaborative International Dictionary of English v.0.48:

Penitentially \Pen`i*ten"tial*ly\, adv.
   In a penitential manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

penitentially
    adv 1: showing remorse [syn: penitently, penitentially,
           repentantly] [ant: impenitently, unrepentantly]