The 26-year-old was the match winner for Villa away from home against Leicester City in the Premier League on Sunday.
Smith is delighted he can call on a player of such quality in midfield thanks to the loan agreement with Chelsea.
He spoke about Barkley post-game and said: "He's a high-calibre player. I'm thankful to Chelsea that they've loaned him to us and I sold him the project here and told him I'll get him in the Euros squad and he's going to try and help us win football games. He's certainly done that in his first couple.
"The doc (Ricky Shamji) has looked after him the past week. He's had a bit of a knee injury and he was touch and go as to whether he was going to start. He only trained on Saturday. He's done a lot of work with the Doc who nursed him through a 90-minute winner. I've certainly thanked the Doc as well."