But Carson insists that King, who has vowed not to quit, has the full support of the club's board.
The former jockey told PA Sport: "It's not been a good start. We're aware of what's been happening but at the moment Andy King is the manager.
"It's like everything else, everybody's position comes in to trouble when you keep losing.
"The board is going to be talking about it at the moment, but if things don't pick up then you never know.
"I think it's best that I keep quiet about the small minority of fans that have been making their displeasure known, even though it will probably continue to happen if we keep getting beat."