Heading into the final round of Group D fixtures, Australia knew a draw with Denmark would secure a place in the last-16 as long as Les Bleus did not lose to the Tunisians.
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However, on 58 minutes, the unthinkable happened and Wahbi Khazri put Tunisia in front against the world champions.
The Socceroos were suddenly facing elimination due to an inferior goal difference, having lost 4-1 to a full-strength France in their opening game.
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Luckily, Mathew Leckie popped up with a huge goal two minutes later to ensure Australia kept control of their own fate with a 1-0 victory and progressed to the knockout stages for only the second time in the nation's history.
But Meulensteen, the former Manchester United assistant, admits it would have been outrageous if the nine changes made by France influenced who finished second in Group D.
The Dutchman also revealed the team did not believe it when they were informed about the Tunisia goal.
"It would have felt an unbelievable injustice," the Dutchman told talkSPORT.
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"We had made one substitution and someone whispered in my ear, 'Tunisia have scored, they're 1-0 up'.
"At that moment in time, I didn't say anything to Graham [Arnold], but in the two minutes after that, we scored.
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"I then told Graham that Tunisa had scored, we needed to win the game, keep a clean sheet and think about the substitutions.
"Then I said to Milos [Degenek], 'Get all the players in a huddle and tell them Tunsia are winning'.
"The funny thing was, because Milos is a bit of a clown sometimes, they didn't take him seriously. They thought he was joking!
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"He had to really convince them and eventually they put their bodies on the line."