Everton's Ronald Koeman became the third managerial casualty of the season on Monday, but Smith said Hughes did not have reason to worry just yet.
"Mark will be working hard to get back to winning ways before anybody does get trigger-happy," Smith told Stoke's Sentinel newspaper. "He's working for somebody who isn't that way inclined and that helps to settle the dressing room."
Smith, who played nearly 500 games in 17 seasons for the Potters and won the 1972 League Cup, said Hughes's senior players could help him retain the faith of the squad.
"There's good pros when you think of players like Ryan Shawcross, Darren Fletcher, Peter Crouch and Jack Butland. They are the kind of players who can stamp down on any such nonsense (player unrest), if ever there was any, and for a manager that is always reassuring to know," said Smith.
"He does have good people behind him. Mark is just the pinnacle of a well-organised backroom staff. That helps."
Stoke will have their task cut out against Watford, who beat top four contenders Arsenal 2-1 in their last home game.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
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