Manager Smith told his club's official website: "I've seen the incident once since the game and Kyle's tackle was a forward's challenge.
"Everyone keeps saying the referee should have acted but the referee did act. He deemed it a yellow card offence and that was it.
"Over the last few seasons, we've gone to Celtic Park for some high-profile games and there have been some meaty challenges.
"This one seems to have attracted a lot of attention when a lot of others seem to have been ignored.
"I think there was a level of frustration in Kyle's challenge but the referee made his decision on it.
"It wasn't a great tackle to make but it wasn't the first time that kind of thing has happened in a football match.
"To be fair, Celtic got on with the game. I didn't see anyone from their side complaining bitterly about it. They just got on with things and we need to move on now."