Phogat was set to face American Sarah Hildebrandt for the gold medal on Aug. 7 but was found 100 grams (3.5 oz) overweight despite starving herself and spending hours in a sauna the previous night to cut down to her competition weight.
The disqualification meant Phogat did not receive a medal and she filed an appeal in sport's highest court challenging the decision of governing body United World Wrestling.
She sought a ruling awarding her a shared silver medal but those hopes faded after the CAS decision on Wednesday.
Cuba's Yusneylys Guzman Lopez replaced Phogat in the final, which Hildebrandt won 3-0 to take the gold.
An emotional Phogat had said after the disqualification that she would retire from wrestling.
