Liverpool chief executive Rick Parry could suggest to football's governing bodies that teams be allowed to use a fourth substitute in extra time.
Parry said the FA Cup final was too tense for him to enjoy
At present only three replacements are allowed during a match - with no concession for the added-on 30 minutes.
Parry came up with the idea after Liverpool beat West Ham in the FA Cup final after 120 minutes plus penalties.
"Here's a thought for the future, maybe a fourth substitute to be allowed in extra time," he told Radio Five Live.
"It would make it less of a lottery."
Several Liverpool players, including captain Steven Gerrard, were struck by cramp in extra time while West Ham striker Marlon Harewood was injured and unable to put any weight on one leg.
"Maybe the issue should be raised with the Football Association," said Parry.
"Poor Marlon Harewood played so well in the 90 minutes but was a passenger at the end. That's no way to decide big games."
Harewood might have won the Cup for West Ham at the death but the ball fell to his injured foot and he sliced wide.
However, Parry feels reintroducing a replay for the final is unrealistic.
"Looking at the calendar, I think we've gone beyond that now," he said.
"Penalty shoot-outs are nerve-jangling and you always feel sorry for the losers but at the end of the day, they produce fantastic drama, talking points and entertainment.
"I think we have to accept finishing it on the day - but it's cruel after two sides have given their all for 90 minutes."