Smith, who is now a pundit for local radio, played for Stoke between 1967 and 1982 and is backing them to defy the odds and survive in the top flight.
He told the BBC: “I think they will be bottom half but not bottom three, and that’s good enough.
“They’ve got enough about them and enough ammunition to cause teams problems and pick up the points they will need.”
Smith added: “The Britannia Stadium is already getting a reputation as a place where teams don’t want to play.”
Watford boss Javi Gracia does not think Abdoulaye Doucoure's form will be affected by his omission from France's latest squad.