Source : Webster's Revised Unabridged Dictionary (1913)

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.

Source : WordNet®

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