The boss revealed Barkley had been “touch and go” to start at the King Power Stadium after struggling for most of last week with a knee problem.
But after returning to training on Saturday, the on loan Chelsea midfielder promptly fired home the only goal at the King Power Stadium one minute into stoppage time.
Barkley celebrated by running to the bench and hugging Villa’s doctor Ricky Shamji and Smith explained: “The doc has looked after him the last week. He has had a bit of a knee injury and it was touch and go whether he was going to start.
“He only trained on Saturday. The doc has nursed him to 90-plus minutes and scoring the winner so that was the reason for the celebration. I’ve certainly thanked the doc as well.
“Ross couldn’t have started any better for us. Being an Everton fan and getting that win against Liverpool and then scoring the winner in the 91st minute.
“It was a tough game for us but that bit of quality showed through in the end.”
Barkley’s 25-yard strike prevented the match from becoming the Premier League’s first 0-0 draw of the season.
Smith continued: “It was a scrappy game at times. I thought they started the better team the first 15 minutes and we had to change things in midfield, go man for man, as they played through us a bit too easy for my liking.
“I thought we grew into the game and were the better team in the second half. A few of our counter attacks we could have done better with the final ball but it needed a bit of quality to win the game and Ross showed that at the end.”
Victory means Villa have won their opening four league matches for the first time since 1930 and they could go top of the Premier League for the first time since 2001 if they take a point from Friday’s visit of Leeds.
But Smith is refusing to get carried away. He added: “We will just take it one game at a time, as always.
“We never get too high when we are winning, just like we never got too low when we were fighting relegation last season. We will certainly try and stay on an even keel.
“I have a lot of admiration for Leicester. This was a big win for us because they are a very good team.
“I know they had some players missing but if you are off it in the Premier League, on any day, you get a bloody nose very quickly.”