He agreed, though, that the midfielder had crossed the line when he was sent off for clattering Ross County manager Derek Adams on Saturday.
Jefferies handed the versatile midfielder his debut at Kilmarnock before taking him to Tynecastle in 2011.
"Jamie sometimes has an edge about him," he said. "There is a bad side to that but it can also be positive when people play on the edge.
"He's got an arrogance about him that is sometimes a good thing on the pitch. But you can't get away with that."