Smith feels the Scottish Professional Football League should exert some influence with main sponsor Ladbrokes.
The former Aberdeen boss, who is the head of the Scottish League Managers Association, was speaking after Ian Baraclough's departure from Motherwell.
"The game needs investment and finance to improve, so I'm sure nothing will change," he said.
"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.
"I will bring the matter up at the next meeting with the league but I'm pretty sure they will say that there is little they can do about it."
The SPFL said such betting activity was "nothing new".
Smith, a player in the 1950s and 60s, began his managerial career at Stenhousemuir before spells in charge of Stirling Albion, St Mirren, Aberdeen, Clyde, Dundee United and Ross County.
Motherwell and Baraclough parted company on Wednesday with the Steelmen third bottom of the Scottish Premiership and having been knocked out of the Scottish League Cup by Greenock Morton on Tuesday.
Odds on how likely each Premiership manager was to be dismissed were publicised earlier in the week.
"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," said an SPFL spokesman.
"This sponsorship received unanimous approval from member clubs in June. Clubs all across the world have their own in-house agreements with bookmakers who promote similar offers."
Meanwhile, Partick Thistle manager Alan Archibald does not foresee an end to bets on manager sackings.
"It's just the way it is," he told BBC Scotland. "I don't think there's any way they'll change it."
Thistle are still looking for their first win of the season and have failed to score in eight of their nine matches but Archibald claims he does not look at the bookmakers' odds on him losing his job.
"There's no point," he explained. "I don't think you'd sleep at night if you worried about things like that.
"It's just the nature of the beast. That's the game we're in always knowing that's what happens.
"Every manager knows if you don't start well you'll be under pressure."
Falkirk director Alex Smith wants to see an end to bookmakers taking bets on which manager will be sacked next.