The Collaborative International Dictionary of English v.0.48:

Inconsequential \In*con`se*quen"tial\, a.
   Not regularly following from the premises; hence, irrelevant;
   unimportant; of no consequence. --Chesterfield. --
   In*con`se*quen"tial*ly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inconsequentially
    adv 1: lacking consequence; "`You're so beautifully dressed,'
           she said and added quite inconsequentially, `Can you stay
           the night?'" [syn: inconsequentially, inconsequently]
           [ant: consequentially]