Petrov said: "We all feel we're on the verge of achieving something special here over the next few years.
"We don't want that to happen of course and, looking at his comments, he has made his position clear. He is staying at Villa.
"That's music not just to the ears of the Villa fans, but the players and staff here as well. I can honestly say he is one of the most charismatic people I've ever met."
Petrov added: "At Villa we are a young, emerging team and Martin has brought in players who will only improve over the next few years.
"Understandably, then, we're desperate for him to stay because he is the one bringing it all together and we all feel we need him behind us to help us achieve the success we all crave.
"I've worked with a lot of managers in my career, but he is definitely the best. I believe he's proved himself in the season or so he's had at Villa.
"Personally, he's been the single biggest influence on my career. I spent six years with him at Celtic and he has done a lot for me."