Source : Webster's Revised Unabridged Dictionary (1913)

Unimportance \Un`im*por"tance\, n.
   Want of importance; triviality. --Johnson.

Source : WordNet®

unimportance
     n 1: the state of being humble and unimportant [syn: {humbleness},
           {obscureness}]
     2: the quality of not being important or worthy of note [ant: {importance}]