Owner Mike Ashley appears to have become tired of Barton's constant criticisms of the club on Twitter, and has taken the unusual step of allowing a player with a market value to walk away for nothing.
McKay revealed earlier this year that his client would not be offered a new deal with the club beyond next summer and, despite acknowledging the role Ashley and managing director Derek Llambias have played in rehabilitating Barton following a number of disciplinary problems, he believes they are making a costly error.
"I was totally surprised when they never offered him a contract," McKay told talkSPORT.
"I think it's a wee bit suicidal by Newcastle because how would you let your player of the year leave on a free transfer, approaching his prime.
"He had a great season last year and he was, for me, pivotal for the club getting £36million for Andy Carroll because he passed every ball to Andy Carroll, for every goal.
"He's a very good player and approaching his prime. I just can't understand what Newcastle are doing.
"Derek Llambias and Mike Ashley stood by Joey when he was under real pressure so I'm not going to come out and slag off Newcastle's board but I think they have made a mistake. He was going to take a drop in wages to sign a new contract."
The root of Barton's public displays of unrest can be traced back to the sale of Carroll to Liverpool in January.
It was thought that the one-cap England midfielder was considering signing a new deal at the time, but decided to put his future on hold until the summer after that.
Then, in May, McKay said Barton would not be offered a new deal, with the player later tweeting that Newcastle wanted a "younger, better, cheaper player".
His discontent was not aided by the sale of close friend and club captain Kevin Nolan to West Ham, and following Sunday's 3-2 friendly defeat at Leeds he took another swipe at club officials.
In the aftermath of full-back Jose Enrique being fined for questioning the club's ambition, he said: "If only we as players could tell the fans exactly how it is, without them above fining us lots of money. There will be a time and a place.
"If it wouldn't effect team morale and cause unrest within the dressing room, am certain Jose's comments would be the tip of the iceberg.....
"And again it would be left to those magnificent fans to pick up the remnants of their once great football club. £hadenoughofcertainpeople.