Tigers began their Guinness Premiership campaign with a 20-8 win at Kingsholm, with tries from Geordan Murphy and debutant Toby Flood.
It was the fourth season in a row that Tigers have won their opening game of the campaign, but Smith said they were already focused on the visit of London Irish to Welford Road for the first home fixture of the season on Saturday.
Smith said: Its only the first game of the season and there is still a long way to go.
We have a lot of confidence off the back of the Gloucester result. Its only one result and this week is a totally different game against a different opposition but its definitely a confidence-booster.
Smith made only his third Guinness Premiership start when he came in at outside centre against Gloucester after Aaron Mauger was forced to pull out with injury.
And the 22-year-old revealed he had expected to play a part as an impact player from the bench.
You come down thinking you will be on the bench and you are thrown in at the deep end, Smith said.
Obviously you love to play. It was a great chance and it was great to play.
There was a lot of hard work defensively and our fitness came to the fore in the last 20 minutes. It was a great win.
Tickets for Saturdays game against London Irish are on sale now. They are available from the Tigers ticket office, by calling 08701 283430 or by emailing [email protected]