Demichelis impressed on his first competitive appearance for his country since November 2011 when Alejandro Sabella selected him to start Saturday's 1-0 quarter-final triumph over Belgium.
The 33-year-old, who played alongside Robben and under Dutch coach Louis van Gaal at Bayern Munich identified the forward as a key threat to the South Americans' bid to reach a first World Cup final for 24 years.
But the Manchester City centre-back believes Robben, who courted controversy earlier in the competition after admitting to diving during the Netherlands' last-16 win over Mexico, does not enjoy physical confrontations on the field and pledged to get "under his skin".
Demichelis told Argentinean newspaper Clarin: "We have to be aggressive, to show the passion of the Argentinian players to the Dutch – and especially to Robben. He doesn't like physical contact, so you have to make him feel it and get under his skin.
"He is a phenomenon and it is vital to know which way he goes. But he's not got much edge, he's not a fighter.
"Therefore you have to attack him because the more you stand off, the nearer to the goal you take him and the less margin of error you have."
Van Gaal ended Demichelis' eight-year stint at Bayern, selling him to Malaga from where he followed coach Manuel Pellegrini to the Etihad Stadium.
Nevertheless, he holds the incoming Manchester United manager in the highest regard and was not surprised to see such a bold move from Van Gaal as bringing substitute goalkeeper Tim Krul on for Jasper Cillessen ahead of the Netherlands' penalty shoot-out success against Costa Rica in the previous round.
"I was irritated [when left out of the side] but I always recognised he was the best football-wise, for the concepts he has and how he imposes them on a team," Demichelis said.
"He has shown that in this World Cup. But I didn't leave because of him, but because of my own decision.
"I've seen him do such things [as the Krul substitution] many times. For example, he'd get in front of the squad and say who was the best or worst at doing different things."
"He has a real determination in thinking about the team and potential consequences. I learned a lot from Van Gaal."
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