South Korea went to the arbitration court after their 1,500m short track speed skater was disqualified from Wednesday's final for impeding America's Apolo Anton Ohno.
But a CAS tribunal met on Friday night and decided to reject the protest.
The South Koreans are still considering taking their case to a US district court.
"Justice has to be done and the judges have to be brought to book - their performance was a scandal"
They have also appealed to the International Olympic Committee over the result.
Meanwhile, South Korea's top Olympic official said his team will not boycott the closing ceremony, despite earlier reports.
The Korean delegation wanted to make a stand over what they perceived to be biased judging.
Park Sung-in said: "Frankly speaking, I want to boycott the games and go back home.
"I can't bear to watch any more of these unfair rulings."
The incident caused widespread anger in South Korea.
The United States Olympic Committee (USOC) received more than 16,000 e-mails in respones to the decision.
Kim's disqualification occurred when Ohno made his move on the last bend, but couldn't get past Kim in front of him.
Ohno raised his arms in protest as his path was blocked by the Korean.
Kim, the reigning champion, crossed the line first and started celebrating, before the officials threw him out of the race and handed the gold to Ohno.
Ohno had previously been involved in a dramatic finish to the 1,000m on Saturday when he was brought down on the last curve after clashing with a Chinese and Korean skater.
Ohno threw himself over the line to take silver, but following the race the USOC received e-mails threatening the skater.
The USOC has turned them over to the FBI, which is investigating.