The midfielder was sent off after 36 minutes for a challenge on George McCartney before Forest went on to lose 4-1 to their npower Championship promotion rivals at Elland Road on Saturday.
An FA Regulatory Commission has upheld referee Mark Halsey's decision and Cohen must serve a three-match suspension.
He will miss Forest's forthcoming home games against Reading and Burnley and the trip to Norwich on April 15.
Source: PA
Source: PA