Accies' Xavier Tomas was sent off for two bookings, with Canning suggesting decisions went against his side.
And his reaction did not go down well with Dons manager McInnes
"Martin's comments that 'being the wee team', they get used to 'playing big teams who get all the decisions' have to be addressed," he said.
"If you look at the facts, they were given a penalty against us here last year which they scored, which wasn't a penalty.
"They got a penalty down there in the 1-0 victory that later everyone deemed wasn't a penalty, so we have been the victims of two penalties against us which shouldn't have been.
"So I think that quashes his argument that they don't get big decisions against the so-called bigger teams."
In the aftermath of Sunday's match Canning questioned the consistency of referee Euan Anderson, insisting Dons captain Graeme Shinnie had made "five or six fouls" yet was only booked once, while Georgios Sarris was cautioned for persistent fouling.
"I do have a problem with the manager's comments about trying to get Graeme Shinnie sent off," said McInnes, whose side visit Hamilton on Wednesday night in the Scottish League Cup.
"He [Canning] is in the fourth official's ears but when you look at it and we have watched the game back, he [Shinnie] has only two minor infringements after being booked and it wasn't the six fouls that Martin Canning [said].
"If I was Martin Canning I would probably be more keen to speak about my own player being foolish enough to be sent off after being booked."
Goals from Anthony O'Connor and Miles Storey gave Aberdeen the three points, but they travel to New Douglas Park having suffered two defeats there last season.
Derek McInnes has criticised Hamilton boss Martin Canning for claiming his side were treated unfairly by officials in Sunday's 2-0 defeat at Pittodrie.