Bayern Munich star Robben won the decisive penalty, converted by substitute Klaas-Jan Huntelaar, as the Dutch completed a dramatic last-gasp comeback to earn a 2-1 win in the World Cup round of 16 over Mexico on Sunday.
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"Simulation is not something we want to see on the field of play but the referees are trained to identify these simulations and punish them by showing yellow cards," Fischer said.
"The disciplinary committee will look into serious infringements. We appeal to the spirit of fair play which is the over-arching message we have."
Robben is set to give a media briefing of his own on Tuesday following the furore caused by his comments and, in a statement on their official website, the Dutch Football Association (KNVB) criticised media interpretations of the winger's interview.
"KNVB is unpleasantly surprised by publications in the media about the Dutch penalty in the match versus Mexico," the statement read.
"Media have interpreted statements from Robben in a Dutch post-match interview completely wrong.
"In a studio interview with Dutch broadcaster NOS, the forward stated that the decision of the referee to give a penalty in the second half of the game was perfectly right.
"However, in the same interview Robben referred to two situations earlier in the match (first half), when he was brought down. The striker stated that in one of those situations he should have been granted a penalty, but that in the other case he was falling too easily."
Netherlands' next World Cup match is a quarter-final against surprise package Costa Rica on Saturday.