Ralph was sent off in the 20th minute of Sunday’s 1-1 draw after fouling Daniel Candeias on the edge of the penalty area.
Though it appeared to be for dangerous play, as Ralph caught his opponent on the ankle with his studs, Dundee boss Jim McIntyre later said that referee Alan Muir had told him it was for “denying a goalscoring opportunity”.
With Dundee defenders between Candeias and the goal at the time of the foul, the club took the decision to appeal the decision against their 25-year-old left-back.
However, they have now confirmed that their bid has failed. A statement on the club’s website read: “The club received confirmation this morning that we have been unsuccessful with the appeal for the red card shown to Nathan Ralph last Sunday.
“Nathan will miss our match against Kilmarnock on Saturday.”