Platini called the politically-charged violence in Belgrade "inexcusable", while Blatter said football should never be used to make 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 two sides 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 spokesman quoted Platini as saying.
"The scenes in Belgrade last night were inexcusable."
Uefa, the European football body headquartered in Nyon in the Swiss canton of Vaud, was expected to formally open an investigation into the events on Wednesday after studying reports from the match referee and coordinator.
"Football should never be used for political messages," said Blatter, president of Zurich-based Fifa.
"I strongly condemn what happened in Belgrade last night."