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Purse was alleged to have pulled back Blades substitute Nick Montgomery as he ran towards goal.
This was deemed a professional foul which carries an automatic one-match ban that comes into operation 14 days after the offence has taken place.
Purse will therefore be available for both legs of the play-off semi-final against Millwall but if Blues win the tie he would be suspended for the final on May 12th.
Straight after the game on Sunday, Blues boss Steve Bruce had questioned the referees decision to show Purse the red card but was waiting to read his report before taking the matter any further, but referee Phil Richards will not be changing his mind on his initial decision.
If Blues fail to reach this years play-off final then the automatic ban will come into effect at the beginning of next season.