Smith complimented Barkley for his ability to settle into the team quickly after joining Villa on a season-long loan from Chelsea.
After victory at Arsenal, Smith said: "Good players, they can play with each other very quickly - they don't need time to work each other out.
"We are seeing that with Jack and Ross, both technically gifted footballers but have the work rate as well.
"Ross was a marquee signing for us, he wanted to get game time to get in the Euro squad. His performances will be nudging Gareth Southgate."