And the Bulgaria international is hoping O'Neill will be able to bring in new signings during the summer to further strengthen the Villa squad.
O'Neill has already confirmed that he will "discuss everything" with club owner Randy Lerner at the end of the current campaign.
But the former Celtic boss has strongly hinted he will complete the rebuilding job that is already under way at Villa.
When asked about O'Neill's future, Petrov said: "I've said before I am not worrying about that and nothing has changed.
"Martin is someone who, when he starts something, he wants to finish it so I'm hoping he will be here in the summer.
"As for signings, it is always good to strengthen the team and we hope we are going to see new faces coming in to improve and to make us better."
Villa's hopes of winning silverware ended with the 3-0 FA Cup semi-final reversal against Chelsea on Saturday.
Villa can claim with every justification to have been denied a clear-cut penalty early in the game when John Obi Mikel brought down striker Gabriel Agbonlahor, although referee Howard Webb thought otherwise.
It added to their frustration after Phil Dowd failed to send off Manchester United defender Nemanja Vidic in the Carling Cup final when, as the last defender, he brought down Agbonlahor in the box.
But Petrov also believes Villa have themselves to blame for Saturday's outcome before goals from Didier Drogba, Florent Malouda and Frank Lampard gave a flattering look to the final scoreline for the Blues.
He said: "It is not the best feeling at the moment but it's football. We are very disappointed. There were a lot of heads down after the game because we felt we deserved more from the game and we got nothing.
"Decisions didn't go our way. At the end of the day, that's football and we need to blame ourselves.
"You have to score goals to win games. We didn't manage to do that, they scored three and went through.
"What can we learn? When you get chances, you need to take them because teams like Chelsea, when they get even half a chance, they take them."
Petrov is confident Villa's season will not fade out and they will still push hard for a European spot ahead of Wednesday's home clash with Everton.
He said: "It won't be hard to bounce back. We know what people expect. We showed at Wembley that we can come back after a very heavy defeat against Chelsea a couple of weeks ago in the league.
"We played really well and we are going to kick on. We've got another game on Wednesday and we are going to try and qualify for Europe.
"That is the ambition now. That will drive us on.
"I said before the Carling Cup final that we could have a great season and end up without anything. We need to make sure we end up with something we can celebrate.
"After losing the final and the semi-final, it has made us even stronger to get there."
Drogba opened the deadlock midway through the second period - his 32nd goal of the campaign - then Malouda and Lampard scored in the dying minutes as Villa pushed in vain for an equaliser.