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]

Moby Thesaurus II by Grady Ward, 1.0:

38 Moby Thesaurus words for "unimportance":
   daintiness, delicacy, diminutiveness, exiguity, exiguousness,
   fewness, homeliness, humbleness, humility, inconsequentiality,
   inconsiderableness, ingloriousness, innocuousness, insignificance,
   insufficiency, littleness, lowlihood, lowliness, meagerness,
   meanness, meekness, minuteness, moderateness, modesty, pettiness,
   picayunishness, plainness, poorness, puniness, scantiness,
   simpleness, slightness, smallness, submissiveness, teachableness,
   tininess, triviality, unpretentiousness