The captain on Tuesday signed a new five-year contract to sign for the Premier League club until he was 30.
Grealish has been at Villa Park since he was 8 years old and made 187 first-team appearances, scoring 26 goals.
Villa Sheffield United receive in their first main league match on Monday, and Smith, who signed Bertrand Traoré of Lyon on Saturday, has told Grealish to continue running the league for a long time.
“First of all, it’s worrying to think of Jack as a 30-year-old,” he said.
“I have already said that we have high hopes that we can continue to grow as a football club. We maintained our prestige last season, now we’re going to keep building on that. “
“Homeowners have commented on their position over the next 4 or five years and that will have to be our goal.
“There are very few men in a club. Steven Gerrard comes to mind. JT (John Terry) would have seen the softness of the burgundy and blue for a season. There are very few of them. “
“I just like the fact that he sought to worry and then did it for his club, his village, his house.
“He has already lived the dream of all young people by being a fan and leading them to the promotion at Wembley.
“He to pass extra now. “
After Grealish signed his new contract, Smith added Lyon Traoré forward for about 17 million pounds for approval.
Burkina Faso’s foreigner began his career at Chelsea and ceded to Vitesse and Ajax.
The 25-year-old is stepping up Villa’s attack after Ollie Watkins arrived from Brentford for a club record of 28 million pounds this month.
Smith told the club’s website: “We are very happy that Bertrand has chosen to come to Villa.
“He’s a player with great skill who will really have our attack options. “