While the initial incident was missed by the referee on the field, the VAR called his attention to a matter where it appeared that the Danish forward had handled the ball in his own box.
The referee decided to award the penalty to the Soceroos, with Mile Jedinak scoring his second spot-kick of the tournment.
But Republic of Ireland manager Martin O'Neill was enraged that the call was given in favour of the Australian team.
While speaking as a pundit on ITV, O'Neill said:
"I genuinely don't think it's a penalty. What is Poulsen going to do with his arm, get it cut off? Send the doctor on?
"I'm sorry its an impossibility to pull out of it and its not a penalty,"
VAR has again proved to be a controversial addition to this year's World Cup, with the Northern Irishman adding that he thinks the process of the referee viewing the technology is flawed.
"The referee gives the penalty after he's gone to the VAR and I actually think as he makes that walk across there he's under pressure [to give the penalty]."
The match in question ended in a 1-1 draw, with Denmark moving to 4 points in Group C while Australia managed to earn their first point of the tournament.