Smith told the club’s official website: "The main thing was getting through, I felt we were a bit disjointed in our play but when you make as many changes as we did then that can happen.
"It took us a little bit of time to get started but once we got the first goal we settled down a bit.
"It was a great goal from Andy Little which gave us the lead.
"He started the game at right midfield and then we moved him up front. He plays right full back too so we will have to pin him down at some stage or another.
"It was certainly a finish that any centre forward would have been proud of.
"Kilmarnock started the second half very well and that was their best spell so we go our second goal at the right time to give us that bit of comfort."
Smith had hoped to field Kyle Lafferty and Andy Webster in the match but both were late call-offs.
The manager said: "Kyle could not make it because of a stomach bug and Andy Webster couldn't play because of a groin strain yesterday."
Smith gave a first start to Gregg Wylde who set up Naismith's goal and also introduced Kyle Hutton for another taste of top team action.
He added: "I was pleased with Gregg Wylde's first start for the club. He has made one or two appearances for us but it's always a bit nervous when you start for the first time.
"We gave another chance to Kyle Hutton and we were happy to put him on."