CAS says the photo-finish ruling was a "field of play" decision by International Triathlon Union race officials and cannot be challenged.
The court says such decisions are "unable to be reviewed by CAS panels" unless they were made in bad faith.
The ITU studied the photo-finish before declaring Nicola Spirig of Switzerland had broken the tape first.
Spirig and Norden finished side by side and were given the same time at the end of a 1,500-meter swim, a 43-kilometre bike ride and a 10-kilometre run in Hyde Park last Saturday.
The Swedish team wanted both athletes to be given a gold medal.