The Blues midfielder was given a straight red card by referee Uriah Rennie just 28 minutes into the game at Anfield for his mis-timed, but not seemingly malicious, tackle on Reds defender Daniel Agger.
Blues boss Steve Bruce was upset with Rennie's decision to dismiss Johnson and was hoping that the referee would reverse his decision.
Should Blues not appeal the decision then Johnson will face an automatic suspension for the sending-off meaning he will miss the games against Arsenal (h), Reading (h) and West Ham (a).