Sheridan, 52, was sacked in January, 23 days after a verbal outburst at officials during the Magpies' 2-0 defeat by Wycombe on 10 December.
The ex-Republic of Ireland midfielder also received a five-game ban.
"I am not prepared to tolerate any member of my staff abusing referees and officials in this manner," Hardy said.
Hardy, who took over the League Two club in January, added: "The conduct shown by Mr Sheridan towards the match officials in this instance was nothing short of scandalous. Mr Sheridan and the LMA are effectively trying to run a coach and horses through the concept of respect,
"I was astonished to receive notification from the LMA that Mr Sheridan has decided to appeal his dismissal."
The Football Association report, released following the fixture, revealed Sheridan had used foul and abusive language towards referee Eddie Ilderton and fourth official Matthew Donohue.
"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," Hardy continued.
"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."
BBC Sport contacted Oldham but Sheridan was unavailable for comment.
The League Managers' Association, who are supporting Sheridan's appeal against the terms of his dismissal, said in a statement: "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."
Notts County chairman Alan Hardy is 'astonished' by former manager John Sheridan's appeal against his dismissal from the club for gross misconduct.