The only goal of the two legs, scored by Ricardo Rodríguez from the penalty spot on Thursday after Corry Evans was controversially adjudged to have handled when the ball struck the back of his shoulder, proved to be pivotal.
This will be Switzerland's 11th qualification to the FIFA World Cup after making their debut at the second edition in Italy in 1934.
Northern Ireland saw their World Cup dream die in Basel on Sunday evening, though it was a controversial penalty three days earlier that ultimately sent Switzerland through to Russian Federation. For a thrilling half-second the ball was going in and the game was going to extra-time. They should have killed off this match rather than hanging on desperately at the end, hoping their visitors did not take it to extra time.
Switzerland began the second half much like they ended the first and crafted a chance with 60 seconds - Zuber taking too long and seeing his eventual shot blocked after Stephan Lichtsteiner picked him out in space at the back post.
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Switzerland were quicker and stronger and started to create the better chances, but could not finish Northern Ireland off. Zuber failed to turn in a Shaqiri cross, Gareth McAuley had to stab away Blerim Dzemaili's cross, Haris Seferovic hit one into the side netting. Tonight we played with raw courage.
Seferovic glanced a free header wide and shot wide of the near post as the Swiss began to take control.
O'Neill, who wouldn't be drawn on his own future, was quick to point to the gulf between the two sides and what that said about his team's character and spirit.