The Swiss needed a two-goal victory but could find no way past a Honduras side who also leave South Africa, without a goal following defeats to Chile and Spain who progress to the last 16.
Both sides had numerous chances and Honduras - who only had an outside chance of qualifying - could feel unfortunate they did not emerge winners as the game opened up into an end-to-end affair towards the end.
But it was ultimately a frustrating night for Ottmar Hitzfeld's Swiss side, who had defeated European champions Spain 1-0 but then lost 1-0 to Chile and lacked the penetration when it counted to get the goals they were looking for to go through.
In Image: Honduras' Walter Martinez, right, has a soccer ball under his jersey as he applauds with teammates at the end of the World Cup group H soccer match
Coverage: FIFA World Cup