Villa had looked on course for a win after Stewart Downing's header gave them a first-half lead.
Kenwyne Jones, however, headed an 80th-minute equaliser and a late Robert Huth winner left Petrov cursing Villa's inability to hold on.
"I didn't think that we deserved that," he told AVTV.
"But at the end of the day it's up to us players to make sure we see games through.
"We defended well, we were well organised, we played some good stuff and we scored a great goal to give us the lead.
"We looked comfortable and they were just playing long balls.
"It was so disappointing to see us eventually go down and lose the game in the last 10 minutes.
"Their first goal was a great header. I can complain about the second one because a few things went against us.
"But at the end of the day, we can't blame this and that but it's up to us to see the game through.
"We played well but we need to be more clinical. We got the important goal and then we needed to see it through - but we couldn't. In this league, if you don't, you get punished.
"The dressing room is down because we put in a lot of hard work. When you do that and get nothing from a game, it's very disappointing."
Villa will host Bolton this Saturday and the Bulgaria international is backing his team to have an upturn in fortunes.
He added: "We can bounce back from a game like that. The next match will come around quickly and we need to be ready for it."