The 26-year-old had been an injury doubt before the 1-0 win at the King Power Stadium but found the net from the edge of the area in added time.
Villa, who thumped Liverpool 7-2 before the international break, have won their opening four games of a league season for the first time since the 1930/31 campaign.
They sit second in the table, a point behind leaders Everton but with a game in hand, a remarkable turnaround after avoiding relegation on the final day of last season.
“Ross showed why he’s a very coveted player with a finish we’ve seen him do a number of times,” said Smith. “He’s a high-calibre player. I’m thankful to Chelsea that they’ve loaned him to us.
“I sold him the project here and told him I’ll get him in the (England) Euros squad and he’s going to try and help us win football games. He’s certainly done that in his first couple.”
Smith said Barkley, who has formed an impressive partnership with Jack Grealish in midfield, had made an immediate impact at Villa and brought extra quality to the side.
“Getting a goal as a Blue (former Everton player) against the Reds (the win against Liverpool) and the winner in the 91st minute, it couldn’t have gone any better for him,” said Smith.
Barkley is thankful to Smith for giving him time on the pitch — he made just 28 Premier League starts in a Chelsea shirt after arriving from Everton for £15 million ($20 million) in 2018.
“The manager has given me the platform to play and I am excited and looking forward to every game,” said the England man.
– ‘Trying to make history’ –
Barkley dedicated his goal to team doctor Ricky Shamji, to whom he ran after scoring.
“He’s had a bit of a knee injury and he was touch and go as to whether he was going to start,” said Smith.
“He only trained on Saturday. He’s done a lot of work with the doc, who nursed him through to a 90-minute winner.”
Smith, who guided Villa to the League Cup final last season, said he would try to keep his players’ feet on the ground.
“I said to the players at the start of the season we’re all about trying to make history,” said the Villa boss.
“We done it in my first season (2018/19 in the Championship), winning those 10 (consecutive) games and we stayed up last season.
“It’s important we keep our feet on the ground and stay humble.”
