He said: "We've not taken that many defeats and we have always had a good reaction from our group overall.
"Certainly we will have to get a good reaction from them on Saturday.
"All the games are important and performances are important. Tonight, in the first half especially, it wasn't good enough.
"I thought St Johnstone were excellent in the first half and I'm disappointed that my team didn't match that."
Smith added: "We don't seem to lose two goals or anything like that. We seem to go from not losing any or losing one to losing three or four.
"They were poor goals tonight from our point of view and St Johnstone will be happy with the manner in which they got their goals."
However, Smith did not feel complacency had a part to play.
"I don't think so," he said.
"I don't take anything away from the way St Johnstone played tonight. They set about the game well as the majority of teams do against us at any given time in the year but normally we have a better reaction to that.
"Tonight we lost a couple of poor goals defensively but you can't take anything away from St Johnstone - they were brighter and more aggressive than we were.
"The disappointing thing was that they are striving to get into the top six and we are striving for the championship but they looked keener and were more aggressive than we were in the first half of the game."