The 28-year-old pleaded guilty to the charges from the Hampden hierarchy, which included a bet placed, as part of an accumulator, on Rangers to draw at East Stirling in April.
He has banned for three games and handed a £7500 fine and Smith, who could make his debut against Arbroath today, has backed Black.
He said: "To be honest with you, everything is the same.
"We spoke about it, but I'm not going to come in here and actually say what we spoke about.
"We like having Blackie here, we like him in the team, he gives 100%. I don't really know too much about it, to be honest, but we are delighted to have him here.
"He gives his all every day in training and he gives his all in every match and that's all we can ask of him
"No [betting against the club is not an issue], not at all.
"I've trained with him every day for the last two or three months, playing as well, and he has given everything he has got.
"I have known him for a long time, in fact, I have played with him or known of him since he was 15-years-old.
"Every team he has played for he has always given everything he has got. That is all we can ask for as team-mates.
Smith added: "100%, no question, we trust him."