Smith was speaking after Ian Baraclough was shown the door by Motherwell following their defeat in the League Cup by Championship side Morton.
Less than an hour after the final whistle at Cappielow Ladbrokes was offering odds on Baraclough being the first Premiership boss to be dismissed.
“The game needs investment and finance to improve, so I’m sure nothing will change,” Smith told BBC Scotland.
“I would ask bookmakers to take into consideration the people on the receiving end of it and try a different approach to take that undignified element away from it.”
An SPFL spokesman said: “The market offering the odds on the next manager to leave a club is nothing new and indeed existed a long time prior to the SPFL welcoming Ladbrokes as its title sponsor.”