Smith is delighted with Barkley's impact.
"He's made a big impact," Smith said.
"The fact that we've gone out and managed to entice that calibre of player into the squad has certainly gone down well in the dressing room and with our staff and fans as well.
"He's a top player, who has been in and amongst the Champions League for the last two or three years of his career. He's been a regular starter for England too.
"He's not played the amount of minutes he's wanted to [at Cheslea], and we've managed to get him to Aston Villa. His job now is to produce performances for Aston Villa that take the eye of Gareth Southgate and get him back into the England squad."