Shearer, who scored 206 goals in 404 games for the Magpies, told The Sun last week that the appointment of Kinnear had "undermined" manager Alan Pardew and said recent events at St James' Park had turned the club into a "laughing stock".
Kinnear responded angrily to Shearer's comments in an interview in the Sunday Times, and highlighted the former England striker's failure to keep Newcastle in the Premier League in the final eight games of the 2008-09 season, when he succeeded Kinnear after he had suffered a heart attack.
"What Shearer says is diabolical," said Kinnear.
"This is a guy who hasn't got a clue about coaching."
He added: "The last game of the (2008-09) season he came up with the master idea of playing Damien Duff at left-back. Damien is one of the best left-wingers in the business, but can't tackle. And we went down with an own-goal from Damien.
"Shearer keeps slagging me off. He is being disrespectful to me. I am entitled to fight back."