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.
More From This Section
Later yesterday, UEFA announced that it had opened a formal investigation into the events, after having studied reports from the match referee and coordinator.
The Football Association of Serbia is under investigation specifically over the setting off and throwing of missiles, crowd disturbance, a field invasion by fans and the use of a laser pointer from the stands.
UEFA said that the Football Association of Albania was meanwhile being probed under charges of refusing to play and the display of an illicit banner. The case will be dealt with by the UEFA Control, Ethics and Disciplinary Body on 23 October.