Local businessman Hardy took over the Sky Bet League Two club in January, sacking the Magpies boss and installing former Bolton, Newcastle and West Ham midfielder Kevin Nolan as manager.
The County owner later clarified that Sheridan was sacked for gross misconduct rather than the side's poor form following a foul-mouthed tirade at officials during a 2-0 defeat to Wycombe on December 10.
The Football Association dished out a five-match touchline ban and Hardy has let rip at Sheridan, now managing at Oldham again, and the LMA for appealing his dismissal.
Manager Kevin Nolan registers as a player at Notts County
"I was astonished to receive notification from the LMA that Mr Sheridan has decided to appeal his dismissal," Hardy said in a statement released to Press Association Sport.
"We have sent back an extremely robust five page document re-affirming the transparent reasons behind our course of action.
"As well as being owner of Notts County, I am heavily involved in youth football, running a series of teams at Under 8s and Under 10s.
"Every week I see the influence that the professional game has on young boys and girls from as young as six years old.
"The conduct shown by Mr Sheridan towards the match officials in this instance was nothing short of scandalous. I am not prepared to tolerate any member of my staff abusing referees and officials in this manner.
"I fully appreciate that the League Managers Association have a duty of care to represent their membership.
"But surely even a professional body like the LMA realise they are being asked to defend the indefensible.
"Mr Sheridan clearly believes this 'industrial language' is used in everyday workplaces. Not in my place of work, it's not. And nor at my football club.
"The FA clearly felt that it was a case of the gravest nature.
"A five match touchline ban is one of the lengthiest and strongest punishments they have issued to any manager this season.
"For me, this is not just about John Sheridan, the LMA and Notts County.
"This case has much wider significance and repercussions for the English game as a whole.
"Over the past years, the FA have instigated a series of very admirable 'Respect' initiatives designed to improve conduct across the game.
"I'd think we'd all agree that excellent progress has been made but that much more clearly still needs to be done.
"Mr Sheridan and the LMA are effectively trying to run a coach and horses through the concept of respect in football. Potentially, they can set us back years if they continue to appeal the decision.
"Needless to say, we will be contesting any appeal by Mr Sheridan and the LMA, but I do genuinely think people should consider their actions very carefully before embarking on a course which may embarrass themselves in particular and the game of football in general."
The FA made public the foul and abusive comments made by Sheridan towards referee Eddie Ilderton and fourth official Matthew Donohue during December's match with Wycombe.
The report revealed details of Sheridan saying to Donohue ''You're a f****** c***. A c***.'' before shouting at Ilderton ''You're a f****** disgrace, you're f****** useless, you've not f****** got anything right today, you should be f****** ashamed, you're f****** s***, my kids aren't going to get any f****** Christmas presents because of f****** you''.
Press Association Sport was unable to get hold of Sheridan through current employers Oldham, but the LMA responded to Hardy's comments on Tuesday afternoon.
A statement read: "It would be inappropriate for either party to comment in any detail on this matter publicly whilst there is potential legal action pending, save as to say, that our member disputes that the sole reason for his dismissal was gross misconduct.
"Mr Sheridan was dismissed on 2 January 2017 following a 4-0 defeat and on the back of six straight defeats. Mr Sheridan's dismissal took place 23 days and five games after the incident at Wycombe and four matches into his five match touchline ban."
Foul-mouthed rant cost John Sheridan Notts County job, owner Alan Hardy claims
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