Coleman was charged with improper conduct and/or bringing the game into disrepute when he criticised referee Steve Bennett's display during the FA Cup defeat by Chelsea in March.
But he escaped with a warning as to his future conduct and a
£2,500 fine - £2,000 of which is suspended until the end of next season.
Coleman told the Coventry Telegraph: "I am very pleased with the outcome.
"I have to thank Ian Smith and John Duncan from the League Managers' Association who helped me with the case and I have to say that I thought the FA were extremely fair and listened to everything I had to say."