Supporters' groups planned to protest against the influence of Lloyds Banking Group ahead of Saturday's game against Hearts.
Despite claiming plans for the demonstration were scuppered, some banners were visible inside the stadium.
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Hide AdBut Smith, who takes his side to face St Mirren tonight, said: "That has surrounded us now for a long time and I don't think it's going to have any great effect on the team in any way, shape or form. If people want to do that, it's a democratic society and there is nothing we can do to stop it. But it doesn't affect the team a great deal anyway."
Buddies boss Gus MacPherson is seeking a positive reaction in the wake of Saints' defeat to Motherwell at the weekend. He said: "There is pride to be restored and that's what we will be looking to do."