The north east club are currently bottom of the Premier League and have taken just one point from their opening five games.
Allardyce said: "They have been pretty quick in pulling the trigger with the last three managers. If it doesn’t go well then they seem to make a knee jerk decision to change the manager.
"Steve (Bruce) and Martin (O'Neill) in their seasons had a bit longer but I find it very difficult to see where the logic lies in this when there has been a full clear-out of the backroom staff.
"To go through this when the season has just got underway is a huge task for whoever is going to be the new head coach in charge. From my experience they have got a massive job on their hands in who they select as the new manager.
"The new manager then has a massive job on his hand making sure he re-addresses the situation with Sunderland at the moment."