Furthermore, he feels the Irishman should have kept quiet once he had been given the job.
The 66-year-old Kinnear became director of football at St James' Park in June and appeared on a number of media outlets making false claims about his managerial record and claiming he would be in charge of bringing in new faces ahead of the Barclays Premier League season, with manager Alan Pardew not involved.
Allardyce, who takes his West Ham side to face his former employers on Saturday, believes Kinnear was wrong to speak so openly when he was appointed and his comments would have been seen as unhelpful in trying to win over the Newcastle support.
"I know Joe has a huge amount of experience," Allardyce said.
"It depends what sort of role Mike wanted him to fill I suppose. He could have made life easier for him all if he had not made the public statements that he made.
"I think that was probably something he should've sorted out internally between themselves not making a public statement in the way he did."
Allardyce feels the director of football system does have a place in football if all parties are working together for the good of the club.
"I think it depends on the relationship you have or the relationship you build," he added.
"It also depends on the relationship between you, the owner and the director of football. There is no whispers or Chinese whispers behind your back, if you start getting that scenario the director of football becomes a bigger obstacle then a help.
"So in terms of it working it depends on that relationship between you, the director of football and the owner and the liaison that goes on between that. So if that is working in your favour then that can help the football club, help the results and help you."
Whilst the idea of a director of football, and the role they play in the running of a club, is still something of a mystery in England it has been successfully employed on the continent for many years.
Allardyce reckons that the idea of being a manager of a club only remains prominent in the British game.
"The director of football probably works better with a foreign coach because it what they are used to in Europe but a foreign coach is not a manager," he said.
"In Europe he is a coach and those responsibilities are far less than the responsibilities in this country, where we are deemed as a manager.
"You are considered as a coach of the first team and all the structure above that deals with the contracts and the players in and the players out. Not that they don't have an input in that but it's not their responsibility to buy or sell players."