City will host Paul Lambert's men in the third round of the Capital One Cup.
Barry told City's website: "They have a good manager in Paul Lambert. The job he did at Norwich was fantastic. When I saw the appointment, I thought it was a great move for Villa.
'"It is a definite step in the right direction for Villa and I think he deserves time to get things right.
"Things don't change overnight. I have no doubt - having heard about the way he works - that he will turn things round."