"It's disappointing to think perhaps that a boozy lunch, where he thinks things will be kept in house, that that may be their true opinion.
"When everyone's watching he'll say what everyone wants to hear, but when it's behind closed doors in an environment where they think no quotes will be taken, then it comes out."
The All Blacks mentor, who will step down following this year's World Cup, is understood to be livid the throwaway line was made public.
Mitchell anticipates Cheika will allow the banter to go through to the 'keeper as he prepares for a World Cup in the absence of sacked assistant coach Stephen Larkham.
The former winger said it was a necessary move to rid "the opportunity for any ambiguity" but warned them not to arrive in Japan as one-trick ponies.
"They needed to do it if the head of the attack and backs coach isn't on the same page as the head coach — the players will be getting mixed messages," he said.
"But you can't go into a World Cup with just one style of play.
"You've got to have that capacity to play expansively when the opportunity presents or tighten it up to play the clock."
