Former England hitman Vardy has scored in seven straight Premier League outings and is closing in on breaking his own 11-game record of netting in consecutive matches.
Leicester have also won seven successive top-flight games to challenge Liverpool and Manchester City at the top ahead of Sunday's trip to Villa Park.
Vardy scored 24 times when the Foxes won a shock title in 2016 and has 14 goals this term.
His strike in their 2-0 win over Watford was his 94th in the Premier League and Smith remains impressed.
"He is a late grower into the game and is certainly flourishing," he said.
"I think people thought maybe the season they became champions was his big season and might have been the top.
"But he is certainly showing and proving to everyone there is still life in him.
"I see people playing high lines against him and he uses the space in behind really well. I have seen low lines, low blocks and he is still getting in behind teams. He is a handful.
"You just have to make sure your defenders are really good on the day but also stop the supply lines to him. That is one of the biggest things too.
"But they are a very good team with very good players and a very good coach. When you get those ingredients you usually get a very good team."
Villa's own £22million striker Wesley has come under fire for his return this season.
He has scored four times in 15 matches since a summer move from Club Brugge but Smith refused to put any pressure on the 23-year-old.
"The pressure is from the outside, it's not from Bodymoor Heath or the dressing room," he said. "He's a popular figure, and came here with a lot of potential and promise.
"He's still trying to fulfil that potential. Villa supporters want to see honest, hard-working players, and he's one of those.
"He's likeable in the dressing room, unfortunately when you get a big price tag on your shoulders, people expect you to score a lot of goals.
"We won't judge him too early."