Platini called the politically-charged violence in Belgrade "inexcusable" while Blatter said football "should never be used for political messages".
Players from the two sides clashed on Tuesday after a drone carrying a pro-Albanian flag was flown over the Belgrade stadium where the Balkan rivals were playing a qualifier for the 2016 European Championships.
Platini "is deeply saddened by the events in Belgrade last night," UEFA spokesman Pedro Pinto said.
"Football is supposed to bring people together and our game should not be mixed with politics of any kind. The scenes in Belgrade last night were inexcusable," the spokesman quoted Platini as saying.
Blatter added: "Football should never be used for political messages. I strongly condemn what happened in Belgrade last night."

UEFA open disciplinary proceedings against Serbia and Albania
Meanwhile, UEFA have opened disciplinary proceedings against the Serbian and Albanian football associations following the violence that caused their Euro 2016 qualifier to be abandoned on Tuesday.
"Disciplinary proceedings have been opened against the Football Association of Serbia for the setting off/throwing of fireworks and missiles, crowd disturbance, field invasion by supporters, insufficient organisation and use of a laser pointer," UEFA said in a statement on Wednesday.
"Proceedings have also been opened against the Football Association of Albania for refusing to play and the display of an illicit banner,” it added.
The case will be heard by the UEFA Control, Ethics and Disciplinary Body on October 23.

Serbia FA blames Albanians for Euro qualifier abandonment

The Serbian FA (FSS) blamed their Albanian rivals for incidents which forced Tuesday's Euro 2016 qualifier to be abandoned but will press for several dozen home fans who invaded the pitch to be charged, the governing body said.
The politically-sensitive Group I match was halted in the first half when a flag of so-called Greater Albania attached to a remote-controlled drone hovered over Partizan Belgrade's stadium before being grabbed by Serbia defender Stefan Mitrovic.
"It was a well-planned political diversion and, at the end of the day, it was the key factor which led to the match being abandoned," the FSS said in a statement on Wednesday.
"All Mitrovic wanted to do was remove the flag so that the match could continue but the Albanian players attacked him. We also wish to point out that the home Serbia fans displayed no offensive banners at any point in time,” it added.
"However, there is no excuse for the pitch invasion by some individuals and after reviewing the footage the FSS will press charges against the offenders,” it further said.
A brawl between rival players broke out after several Albanian players snatched the flag from Mitrovic and then had to run for cover into the tunnel as the invading home fans attacked them while those on the terraces hurled flares.
After a delay of about half an hour, English referee Martin Atkinson abandoned the game, which stood at 0-0 in the 41st minute. Albania fans had been banned from attending the match.
Serbian media, and the country's foreign minister, put the blame on the brother of Albanian Prime Minister Edi Rama, with some media reporting that he had been arrested in the VIP stands of the stadium with the remote control in his hands.
Olsi Rama, who is a US citizen, arrived in the Albanian capital Tirana on the Albania team plane and said he had been "taken aside" by Serbian police during the melee but not arrested.
"I've never used a drone in my life, only bought my son a toy helicopter," he said.
'It's like a war'

Albania's Litex Lovech winger Armando Vajushi, who was on the substitutes bench when the incident unfolded, told Bulgarian media on Wednesday: "It was like a war. You can't play football in a situation like the one in Belgrade. The whole stadium was filled with Serbian fans.”
"We only had a 50-man delegation that was in the VIP (stand). I can't say if our fan drove the unmanned airplane that waved the Albanian flag. Fans invaded the field and started to hit us. Then we ran to the tunnel but nobody protected us. On the contrary, the policemen beat us!” he added.
"Just before entering the tunnel I was hit by a police baton. He hit me in the knee, but it is nothing serious,” he further said.
Vajushi, 22, criticised UEFA and said the governing body should have prevented the two nations being drawn in the same qualification group.
"It's UEFA's fault. How can they put us with the Serbs in a same group? They shouldn't allow such thing at all. Now they have to award us three points,” he said.
On Wednesday, an Albanian fan group calling itself "The Smugglers" posted pictures on Facebook of a group of men posing with what appeared to be an identical drone, known as a quad-copter.
Under the caption "Deeds, not just words," one of the men, identified as Agron Sadiku, wrote: "This was not my idea, but that of my uncle's son, Egzon Feri. We never believed it would be done so successfully. I am very happy about it."

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