Smith took over from Brendan Rodgers (50) on Monday, who left the club by mutual consent earlier this month with the team second-bottom in the table.
Leicester are among a number of clubs facing potential relegation, with bottom-side Southampton and 12th-placed Crystal Palace separated by a 10 points.
The East Midlands club will face four of these eight teams in the league in coming weeks, with all four matches crucial for their survival.
"The points are there to be won, to grab, to get out of the bottom three," Smith told reporters.
"It's been a season I've not seen before in terms of nine teams involved in the relegation battle. The more we can keep in that, it's not insurmountable to get out.
"I know the players, I've come across them before and come up against them. I felt they just needed a lift. I felt confident we could do that. We've seen great enthusiasm. We're trying to put smiles on the faces and that should lift their confidence very quickly."
Asked if he could be a candidate for the managerial position on a permanent basis, Smith replied, "it's not a conversation we've had.
"It's an interim job. I was watching the Masters in Augusta last week and now I'm back in England. I'm looking forward to the challenge."
Smith will face a stern test in his first game in charge on Tuesday at defending champions Manchester City, who are second in the league standings and have won nine straight games in all competitions.
"What we have to do is go with a game plan and stick to it," Smith said.
"Yes, they're one of the strongest teams in the Premier League, if not the world, but we have to have that belief that we can go there and get a result."
Leicester will be without Harvey Barnes (25) and Ricardo Pereira (29) for the clash against Manchester City, but Smith said midfielder Youri Tielemans (25), who has been sidelined since February due to an ankle injury, is "available for selection".
"He hasn't done a lot of minutes in training so we'll have to see if he's ready to start. He'll play a big part. He and Jonny (Evans) give the team calmness," Smith added.
