Mlambo was sent off in the club's 2-1 victory over Orlando Pirates in the MTN8 quarter-finals on August 27.
The Students felt the decision was harsh and lodged an appeal with SAFA's Referees' Review Committee.
However, Wits CEO Jose Ferreira tells snl24.com/kickoff: "Yes, we wrote a letter to SAFA's Referees' Review Committee but our appeal was turned down."
The Clever Boys, who thumped Cape Town City 3-0 in the MTN8 last-four on Saturday, next visit Polokwane City in the league tomorrow.
Mlambo will complete his suspension against Rise and Shine, while goalkeeper Moeneeb Josephs will start his two-game ban following his dismissal on the weekend.