Speaking to local paper the Sentinel last month after a series of matches where Stoke felt they had been badly treated, Coates said: "We feel we don't always get fair treatment and that is all we are asking for.
"There does seem to be a bias towards other teams
You always feel that because we have a good crowd that gets behind the team, referees seem to think, 'I will show them who's in charge here'."
The FA took a dim view of Coates' comments and charged him with improper conduct.
He denied the charge but has been found guilty at an independent regulatory commission hearing.
An FA statement read: "Following an Independent Regulatory Commission hearing, Peter Coates has been fined £5,000 in relation to media comments.
"The Stoke City chairman was charged with improper conduct in that his comments alleged and/or implied bias on the part of referees and/or brought the game into disrepute.
"Mr Coates denied the charge and requested a personal hearing at which the breach of FA Rule E3(1) was found proven
He was also warned as to his future conduct and ordered to pay £1,500 towards the cost of the hearing."
The outcome is unlikely to please Stoke, who were furious that Swansea manager Garry Monk was not punished for accusing Victor Moses of 'cheating'.
The Potters also feel captain Ryan Shawcross has been unfairly singled out as a player who grapples with opponents in the penalty area.
Source : PA
Source: PA