Here's a list of all the times that Nebraska has lost to teams that are not currently part of FBS. Usually, this is because they no longer exist. As far as I can tell, we haven't lost to a team that wasn't fairly "major" at the time of the game since at least the 1890's; those two KC Medics games are suspect. (Note: Can't guarantee that this list is perfect)
1942: Iowa Pre-Flight School (Stud coaches and players on this team, finished #2 in AP Poll)
1925: Drake (A fairly big program at the time; distinctions include the first college to have lights installed on the football field and thus the first night game, and apparently they were the first team to win multiple games in a day)
1918: Wash U of St. Louis and Camp Dodge (another pretty feisty wartime team)
1909: Haskell (Known at the time as the "Powerhouse of the West")
1908: Carlisle (a top program coached by Pop Warner, starring Jim Thorpe)
1907: St. Louis University
1904: Haskell
1899: Rough year: Grinnell, U of South Dakota, KC Medics
1898: KC Medics and Drake
1896: Butte AC
1895: Grinnell, Butte AC
1894: Doane
1892: Denver AC in 1892
1891: Doane (played them three times that year, we won two of three)