The Frenchman, who also played for Barcelona, also urged Arsenal's players to believe they can create history and win the quarter-final second leg in the Nou Camp against the best side in Europe.
Arsene Wenger's men took a battering in the first leg at the Emirates but emerged with a creditable 2-2 draw thanks to some inspired goalkeeping from Manuel Almunia and a rousing second-half fightback.
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And Petit believes Arsenal could now hold the psychological edge over the Catalan giants.
'Arsenal have nothing to lose,' Petit told the BBC. 'If I was Arsene Wenger I'd tell them that they're on the verge of history.
'Barca are champions and favourites and have everything to lose.'
Petit, who also played under Wenger at Monaco, added: 'If Arsenal can win against Barcelona it will probably be the best result in the club's Champions League history.'
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However, the World Cup winner with France did concede that Arsenal will start Tuesday's match as overwhelming underdogs and warned the Gunners that Argentine superstar Lionel Messi is unlikely to have another quiet game, as he did at the Emirates.
'I think they have maybe a 30 per cent chance to do it,' said Petit. 'Arsenal will be without William Gallas and we saw he was missed on both goals Barca scored. They'll also miss Cesc Fabregas - those are two big blows.'
He added: 'The Nou Camp pitch is much bigger than the Emirates.
'We didn't see much of Lionel Messi in the first leg but in the return Arsenal will have to score, so they will inevitably give the likes of Messi more space.
'It will be very difficult to find the right balance between attacking and defending and that's why I think it will be a huge, huge, sensation if Arsenal can qualify. If Barca play intelligently, you fear the worst.'
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