The sanctions, meted out by an independent UEFA panel, were in response to the racist and violent abuse directed towards England Under-21 players during a match between the two in October.
Platini is already thought to be set to appeal them, and Blatter too is concerned about the message they send. Speaking at a press conference in Japan on Saturday, he told reporters: "Not only racism but discrimination has no place in football and there is zero tolerance for it."
Serbia's Under-21 side will have to play one match in front of no spectators, and the Serbian FA have been fined 80,000 euros - equating to #65,000 - following incidents in Krusevac, with several leading figures condemning the punishments as lenient.
Blatter added: "I just learned yesterday what the (Serbia) decision was and I'm sure we will also take it up with UEFA at the level of governance, that there should be in all football, with every confederation and all national associations strong, harsh punishment when it comes to racism and discrimination.
"I will take up a discussion with the president of UEFA but I don't know if he has an influence on his disciplinary committee."
Many have pointed out that the fine is less than Nicklas Bendtner was forced to pay out in the summer after wearing a sponsor's logo at the European Championships. "I cannot intervene in the disciplinary committee of UEFA. Read between the lines and you have the answer," was what Blatter said when asked about that matter.
The Swiss did, however, reiterate he would like to see a severe punishment handed out.
"I don't know the details of the file which has been dealt with by UEFA's disciplinary committee, only on FIFA's stance against racism and discrimination which is zero tolerance," he said.
"We will ask for details of the file but I repeat we have it in our organisation that there must be very, very strong, strong punishment. But again racism and discrimination is now somewhere in football but it comes not from football it comes from society."
- Sports & Recreation