Carney was sent off during the Red Devils' 29-22 win over Toronto Wolfpack in the fifth round of the Ladbrokes Challenge Cup last month following comments directed at Bailey.
The 28-year-old Australian was subsequently charged with verbal abuse based on race or colour by the Rugby Football League's match review panel, a grade F offence which normally carries a ban of eight matches or more.
Carney pleaded guilty to the offence when he appeared in front of an independent disciplinary panel in Leeds on Tuesday evening but contested the severity of the charge.
A Red Devils spokesman said: "Justin has today pleaded guilty to a charge of misconduct being that, in the game against Toronto Wolfpack on 23 April he used verbal abuse to an opposition player based on race/colour, although he did contest the severity of the charge.
"Whilst Justin has admitted using the offending words in an abusive manner, he did not intend his words to be taken in a 'racial' context. Justin is an indigenous Australian and is proud of his Aboriginal heritage. He stands firm on the position that he is not nor has he ever been a racist."