Smith acknowledged the nerves within the stadium beforehand, as his side aim to retain the SPL crown with two games now left to play.
He said: "If you go for a job interview and it's a job you want, you'll be nervous before you go for it.
"If you go for a league championship and you've got a couple of games to win, you'll be nervous before the games.
"It's natural. You still get nervous and you need to handle that situation. It's part and parcel of it.
"Once we got ourselves in front, I enjoyed it. We played well and there were some good moves in the match. We are delighted, although we know we've got to keep it going.
"In my own mind, I felt that we had to win the three games that we had left to play and I think it's still like that.
"The only thing that changed with Celtic losing [at Inverness]was the fact that, if we do win the games, we win the championship, whereas if Celtic had won during the week, we wouldn't. We still have to win our games and that's the way I'm looking at it."