Overton was found guilty of a level-one breach, the lowest of four ECB directives, for comments he was heard making to Sussex spinner Ashar Zaidi in an English County Championship match at Hove in September.
Both umpire Alex Wharf and Sussex's non-striking batsman Michael Yardy said they heard Overton's abuse of the 34-year-old.
It was reported that Wharf included this in his report, with Yardy giving a written statement in support.
Overton denied saying the words, but Kick It Out chairman Lord Herman Ouseley believes the punishment by the Cricket Discipline Commission (CDC), an independent arm of the ECB, does not fit the offence.
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"My personal view would be that it seems quite outrageous; that the punishment does not fit the offence. It's not only serious abuse and misconduct, it is clearly racially offensive," he told the Guardian.
"If a decision seems quite outrageously wrong, then the ECB could appeal and that goes to another panel.
"In appealing, and voicing its displeasure at the verdict, it can send the message that there should be zero tolerance of such discriminatory conduct."
An ECB spokesman earlier insisted that it remains content with the CDC's handling of the case, and Overton was subsequently selected for this winter's England Performance Programme.
"Craig Overton's selection for the EPP squad would have played no part whatsoever in the CDC's ruling in this matter.
"The ECB refutes any suggestion of interference or bias in the proper disciplinary process.