Robinson has found his game time limited in south Wales since the arrival of Barry-Murphy in June 2025.
He has started just nine league games under the Irishman, having been Cardiff’s top scorer in the 2024-25 season with 12 goals.
“The standards that we expect for the dressing room are internal,” the Bluebirds’ head coach said.
“We’re always judged in public so that’s fine, but for the dressing room and how we work day by day it’s private for us.”
When pushed for more detail of what the breach of standards were, Barry-Murphy insisted it would remain in-house.
“I think it’d be wrong to presume [what the breach was],” he added.
“The supporters want to see certain qualities in their team week to week.
“And we have to make sure that they remain the case day to day and then they have to be private.
“They have to be ours, for ourselves.”