"He's a young lad and he is enthusiastic," said Smith. "I think that's natural. He wants to do well and he will do well.
Naismith limped off late in game after being upended by Zander Diamond, who was fortunate not to be shown a straight red card for the foul.
"He took a kick in the ankle but he's okay," said Smith. Speaking of the challenge, he added: "I thought it was a bit harsh. It was the only tackle in the game and I thought it was a poor challenge."
The victory allowed Rangers to reclaim their place at the top after Celtic suffered a 3-2 defeat at the hands of Hibernian at Easter Road in a match which kicked off an hour earlier than the action at Ibrox.
Asked how he felt about Rangers being league leaders again, Smith smiled: "It would be a lot more comfortable if it was the last game of the season.
"When you look at the clubs below us, I do believe that they are stronger and I don't think Rangers and Celtic will have the same points differential between them and the rest of the clubs that they had in previous seasons."