Spanish official David Fernandez Borbalan ruled out a late Shane Duffy winner and waved away penalty appeals.
West Brom's McClean described the referee as "Austria's 12th man" while O'Neill said the Spanish official was "very poor" in the Aviva Stadium game.
Fifa has begun disciplinary processes.
A Fifa spokesman told the BBC they are probing remarks made by both men and it is understood manager and player have until Friday to respond to the charges.
As well as ruling out Duffy's header, Borbalan also decided against giving the Republic a penalty when Jon Walters went down under a challenge from Stefan Lainer.
"It should count, the referee should have given the goal," the manager said of Duffy's header.
"I personally think it typified the referee's performance.
"The lineman thinks he has given a goal and he's almost up at the halfway line before he is called back."
The Football Association of Ireland declined to make any comment when contacted on Wednesday.
Fifa stated: "We can confirm that disciplinary proceedings have been opened.
"Be informed that two cases were opened: one against James McClean and another one against the coach Martin O'Neill."
A spokesman for the world governing body said there will be no further comment as the matter is ongoing.

The collision took place on Repington Road, near its junction with Bagot Grove, in the Sneyd Green area of the city at about 17:00 BST on 14 April.
The boy, who was from the area, died in Birmingham Children's Hospital on Tuesday.
Staffordshire Police confirmed it was investigating the incident and appealed for any witnesses to come forward.
More on this and other stories from Stoke and Staffordshire

It follows 66 Labour MPs voting to extend air strikes to Syria, a policy opposed by party leader Jeremy Corbyn.
Mr Morgan told BBC Wales most party members were "very loyal" to Mr Corbyn and "few" backed wider military action.
But he said most Labour MPs were "not really Corbynistas", so the party was having to deal with a "new phenomenon".
Speaking on the Good Morning Wales radio programme, Mr Morgan said: "In effect we have two Labour parties and this is a bit of a new phenomenon, so we've got to try to let it settle down and work out what's the best way forward."
Mr Morgan called a suggestion by the Labour MP and former minister Frank Field that the party should have two leaders was "quite clever" but "not very workable".
Mr Morgan's comments came as Labour celebrated victory in the Oldham West and Royton by-election.
Deputy party leader Tom Watson called the result "very, very good" for Mr Corbyn, and urged MPs to "swing behind" their leader after a "difficult week".

A gold medal in the race gives an athlete global recognition. Breaking the world record over the distance ensures sporting immortality.
American Donald Lippincott and Czech Marie Mejzlikova were the first, with Jamaica's Usain Bolt and Florence Griffith-Joyner of the United States the current holders of the crown.
Before the 2016 Games in Rio, at which Bolt and compatriot Shelly-Ann Fraser-Pryce will defend the 100m titles they won in London four years ago, BBC Sport presents a chronological history of world records in the event, showing each time it has been broken and when.
An accessible version can be found here
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.
Republic of Ireland boss Martin O'Neill and winger James McClean face punishment from Fifa for criticising the referee after the 1-1 draw in their World Cup qualifier with Austria.
[NEXT_CONCEPT]
A seven-year-old boy has died in hospital five days after he was hit by a car in Stoke-on-Trent.
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Labour is effectively two political parties, due to the split between its MPs and wider membership, ex-Labour First Minister Rhodri Morgan has said.
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The 100m is arguably the Olympic Games' most iconic event.