Losing a football game stinks, but losing a game where, at the end, you are lying face down in a puddle of mud and the fans are burning effigies of you in the streets? That is an ignominious defeat.
Although ignominious can modify other words, it is nearly always attached to "defeat." It derives from the word ignominy, which means public shame or defeat. Ignominy derives from the Latin in- "not" + a variant of nomen "name."