FIFA president Sepp Blatter on Friday described having penalties to determine the outcome of games as a "tragedy" that ripped the heart out of the game.
"Football can be a tragedy when you go to penalty kicks," he told delegates at the world governing body's annual congress in Budapest.
"Football should not go to one-to-one. When it goes to penalty kicks, football loses its essence."
The winners of two major tournaments last season were determined from the penalty spot: the Champions League, where Chelsea beat Bayern Munich 4-3, and the African Cup of Nations, which saw Zambia beat Ivory Coast 8-7.
Blatter called upon German great Franz Beckenbauer, head of the Football Task Force 2014, to find an alternative to the penalty shootouts.
The task force 2014 has been charged with recommending rule changes, and to come up with another way of deciding matches.
"Perhaps Franz Beckenbauer with his football 2014 group can show us a solution - perhaps not today but in the future," he said.
"Why are the English to blame when Bayern are not able to convert their dominance? Luck was on Chelsea's side this time and that is why they are deserved Champions League winners," Beckenbauer said. "Nonetheless, Bayern was the better team for most parts of the game."
In 1993 FIFA had introduced the "Golden Goal" concept, in which sudden death would apply during extra-time. The rule was abandoned after Euro 2004.