Nicky Bailey was "inconsolable" after his penalty shoot-out miss condemned Charlton to another season in League One.
Swindon will take on either Huddersfield or Millwall at Wembley in next weekend's play-off final after Addicks skipper Bailey blazed his side's second spot-kick over the crossbar.
"I've never been in a more distraught dressing room, everyone is devastated," said Addicks manager Phil Parkinson. "Nicky Bailey is inconsolable, he can't speak. But he has won us many games this season."
Charlton, trailing 2-1 from the first leg, got themselves in front through Simon Ferry's own-goal and David Mooney's strike, and had one foot in the final when Swindon's Gordon Greer was sent off.
But the 10 men levelled the tie through Danny Ward and, when extra time could not separate the sides, Bailey's miss proved decisive.
Parkinson added: "I've just had to tell the lads they have done themselves proud. The performance they put in, in a big game, was tremendous.
"To go out on penalties is cruel, it will hurt for a while, but once that wears away the lads should be proud of themselves."
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