Adam faces a three-match ban if found guilty.
Coates told the Stoke Sentinel: "We feel this is trial by media. We are disgusted.
"Charlie absolutely assures us it was not intentional. We will defend it vigorously. It is appalling."
Coates is said to be particularly aggrieved that other recent incidents that were missed at the time by match officials went unpunished.
Coates added: "We have seen some of the things that have gone on in recent weeks and no-one has been called to account."
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