The Euro 2016 qualifying match was suspended in the 41st minute by referee Martin Atkinson after a drone flew over the ground carrying a flag featuring Albanian national symbols.
A melee ensued involving players and fans after Serbia defender Stefan Mitrovic managed to grab the flag, with riot police deployed to quell the violence.
UEFA confirmed on Wednesday that it had begun disciplinary proceedings after receiving match reports from Atkinson, the security officer and the match observer.
Platini described the incident as "inexcusable" and insisted football should not be involved with political situations.
"Football is supposed to bring people together and our game should not be mixed with politics of any kind," the UEFA president said.
"The scenes in Belgrade last night were inexcusable."
His comments were echoed by FIFA president Sepp Blatter, the 78-year-old taking to his official Twitter account to comment on the issue.
He wrote: "Football should never be used for political messages. I strongly condemn what happened in Belgrade last night."
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