Now the England player, who has one year remaining of his contract, is again the subject of speculation linking him with moneybags Manchester City and Rafael Benitez's Anfield side.
Villa boss Martin O'Neill does not expect Barry to make a decision until after the World Cup qualifiers with Kazhakstan on Saturday and Andorra on June 10.
And Petrov said: "I have said many times before just how important Gareth Barry is to this football club.
"We should give him time to enjoy things because he had a hard time last summer with all the speculation about Liverpool.
"What he did, in coming back to Villa again and making the fans happy again with his performances this last season, was great.
"Of course, we all want him to stay but I believe there should be no pressure put on him to make a decision. He will make the decision in his own time."
Petrov is hoping O'Neill will bring in more players to add to the squad which secured a Europa League spot by finishing sixth in the Premier League.
He said: "The club is moving in the right direction and it is good to qualify again for Europe.
"We will take our break for the summer and hopefully we'll have a few good players coming in as well as keeping the good ones we've already got."