A black commuter was pushed back by what appeared to be a group of fans travelling to the Parc des Princes on Tuesday evening, who also chanted: "We're racist, we're racist and that's the way we like it."
However, Platini said UEFA would not get involved as the incident took place away from the ground.
"UEFA can punish what happens in or around a stadium. In the Metro, what do you want me to do? We can, however, recommend clubs keep a close eye on their fans," Platini said.
The former European Footballer of the Year has been at the heart of UEFA initiatives to rid the sport of racism.
"No to racism" videos, featuring a host of famous footballers lending their support to the cause, are broadcast ahead of European competition games, while Platini's own "Respect" campaign features heavily inside stadia during Champions League and Europa League matches, urging players and fans to respect each other and match officials.
Meanwhile, Arsenal manager Arsene Wenger has branded the incident on the Paris Metro as "pathetic."
"It looked pathetic and dreadful. Unfortunately we always have a recurrence of that. You have to be extremely severe with any incident of that calibre,'' Wenger said.
Asked where the problem lies, the Arsenal manager replied: "[It is] society's problem.''
Wenger continued: "More intelligent people than myself think about that and nobody has found a miraculous solution, it certainly starts from childhood education and an open-minded attitude.
"There is a danger of having radical people in every society. Since I observed youth movements, there are always certain people who are ready for radical solutions and most of the time you have to control them."
Platini also hit out at Arrigo Sacchi after the former Italy coach said there were "too many black players, even in the youth teams."
"What Sacchi said isn't good. We're fighting," Platini added. "It's not easy. There is more and more racism in the world."
Information from the Press Association was used in this report.