Arsenal confirmed on Wednesday morning that the Brazilian centre-back will stay on at the Emirates Stadium for a further 12 months.
The news comes on the back of some questionable displays from Luiz, particularly in last week's 3-0 loss to Manchester City when he was at fault for two goals before being sent off.
Petit, who won the Premier League and FA Cup playing under Arsene Wenger at Arsenal, feels that the decision is reflective of the direction that his former club are heading.
"David Luiz hasn't been a proper footballer for about three years. But I'm not surprised that he has been given a new contract at Arsenal, because I've been very disappointed in relation to the club's activity in the transfer market," he told Paddy Power.
"I've been particularly upset in relation to the defenders. We all know one of Arsenal's major weaknesses is their defence and nothing has changed. This makes me miss Arsene Wenger.
"If I was David Luiz, of course I would sign a new deal and I would also say a prayer of thanks to the Arsenal directors every time I wake up. Even when he last won the Premier League with Chelsea, he's not the same player any more. This guy has lost something.
"To be honest, it's a joke. Find some proper defenders. Are you telling me there are no young talented defenders on the market? I just don't get it."