Stephen Ireland and Nigel Reo-Coker had great chances at either end of the game but both shot wide as Villa had to settle for a goalless draw.
Villa Park has been something of a bogey ground for Chelsea in recent years, with the champions having won on only one of their last 12 league visits.
Petrov said in the Birmingham Mail: "They have beaten a lot of teams, they have a lot of quality, but we stood up to them and played as a team.
"We worked hard and were organised, we had our chances but we couldn't do it. Like I've always said, we need to be more clinical. It didn't happen but we are moving in the right direction."
The result also buried memories of last season's 7-1 hammering by the Blues at Stamford Bridge, with Petrov adding: "We didn't think about that. It showed it was a one-off."