Bradley is upset with the rule because at 11½-4½ down going into the 12 singles, his side needed as many points as possible to try and eke out a win. The score became 12-5 before a ball had been struck.
A remarkable comeback on Sunday saw the US come mightily close to catching Europe but they ultimately fell short, losing 15-13.
“It has to change,” said Bradley after the defeat.
“I have a few ideas but I’m not going to tell you right now. It’s obvious to everybody in the sports world, in this room. Nothing against Viktor. But that rule needs to change by the next Ryder Cup.”
However, his opposite number Luke Donald simply stated: “The rule is the rule and it’s been in place for a long time.
“We have contracts for a reason, a captains’ agreement for a reason, for situations that occur.
“I want to centre it back to Viktor; I would have had absolute faith in him to deliver a point. He couldn’t play. He was gutted.”
The envelope rule was introduced when European players were allowed to enter the biennial contest against the US in 1979.
“The US have used it before, in 1991 with Steve Pate,” added Donald. “That was a tight Ryder Cup, too, 14½-13½ [win for the US at Kiawah Island].
“It happened in 1993; Sam Torrance couldn’t play with an injured toe. The US won that one [at The Belfry].”