The Collaborative International Dictionary of English v.0.48:
Unimportance \Un`im*por"tance\, n. Want of importance; triviality. --Johnson. [1913 Webster]WordNet (r) 3.0 (2006):
unimportance n 1: the state of being humble and unimportant [syn: humbleness, unimportance, obscureness, lowliness] 2: the quality of not being important or worthy of note [ant: importance]