Taylor was sent off in the first minute in Thursday's goalless draw at the City Ground after he caught Forest midfielder Lewis McGugan on the thigh with his studs.
After reviewing the video evidence, the Swans felt they had grounds for an appeal to the Football Association of Wales but an FAW hearing on Monday morning dismissed the appeal and Taylor will now serve the first game of his three-match ban in the second leg at the Liberty Stadium on Monday night.
Despite playing practically the whole game with 10 men, the Welsh side held on to put themselves in the driving seat heading into the home leg.
They could meet south Wales rivals Cardiff in the final after they also drew 0-0 in their away leg against Reading.
Source: PA
Source: PA