The incident happened in a Championship game between the sides on Saturday, November 9.
Barnsley admitted failing to ensure their fans behaved in an orderly fashion and refrained from using abusive language.
The abuse was aimed at McClean because he does not wear a poppy on his shirt for games around Remembrance Day over the murders of 14 unaarmed civilians on in Derry on Bloody Sunday in January 1972.
Barnsley will also have to pay the £2,250 costs associated with the Football Association’s Independent Regulatory Commission’s review.
“Barnsley Football Club has a zero tolerance policy on any form of discrimination and, as such, are immensely disappointed to have been found guilty of violating FA rulings,” a club statement read.
“The club will act upon the case findings and will continue to work closely with the Football Association and (anti-discrimination charity) Kick It Out.
“Anybody found to be involved in any form of discriminatory behaviour when representing Barnsley Football Club face a potential ban from attending matches.”
Creggan-born James reported that he had been “racially abused” to referee Jeremy Simpson in the 32nd minute of the game at Oakwell.
The referee told the fourth official, who informed coaching staff from both teams and also Barnsley’s stewards.
The investigation reviewed video footage of the match where a “significant number of individuals” could be heard chanting sectarian abuse.
It also criticised Barnsley for not doing more in advance of the game to mitigate the chances of abuse being directed at Republic of Ireland international McClean, who had been subject to similar instances in the past around Remembrance Day.
The written reasons of the case read: “The club did nothing in advance of the start of the match or (with the exception of deploying additional stewards to a part of the stadium after the 32nd minute of the match) during the match to address the known, increased risk that abusive and insulting language would be used by individuals within the crowd at the match, and was in fact being used by such individuals during the match.
“Doing nothing – as the club chose to do – to prevent or deter such behaviour was not an acceptable option.”
While the report praised Barnsley’s guilty plea, previous good record and the work they have done since the incident to mitigate anything similar happening again, the investigation was critical of a comment made by the club’s deputy safety officer Peter Clegg after the game.
The report says that, when informed at a post-match meeting of the chanting described by McClean, Mr Clegg stated: “He’s a professional footballer, he should be used to it by now” – something which was determined to be a “serious aggravating feature”.
Mr Clegg has been instructed to undertake an equality and diversity course by the external organisation who employs him, while Barnsley have acknowledged the “wholly inappropriate nature of those words”.
He has been warned about his future conduct and his employers have apologised to Barnsley.
He is still in his role at the club.
Barnsley were given a 15-point action plan to implement, including a review of steward training and planning, and a protocol for all stewards on how to report discriminatory, abusive or offensive chanting or behaviour within the stadium.
They have also been told to liaise with other clubs over best practise to prevent and detect discriminatory and abusive behaviour.
The club must also ensure there is more communication with fans to prevent abusive behaviour, set up a dedicated mobile phone number for fans to anonymously report any abuse they witness and “develop and deliver an appropriate diversity education programme in conjunction with Kick It Out through their work in the local community and schools”.