Both players said they had reached decisions before Sunday's game against the Indians at Legends Field.
"To give Bob Watson and Major League Baseball a chance to hear the story from my eyes is pretty important to me," Duncan said.
Duncan, 28, was cited by Watson -- MLB's vice president of on-field operations -- for "violent and reckless actions" which incited the two clubs to spill on to the field at Progress Energy Park in St. Petersburg.
In the second inning on Wednesday, Duncan slid in spikes high to Rays second baseman Akinori Iwamura, cutting the infielder above his right knee.
Duncan was immediately ejected, and both benches cleared when Rays right fielder Jonny Gomes charged in from the outfield and shoved Duncan from behind. Gomes was suspended for two games and fined $2,000 for violent actions which escalated the incident.
Cabrera was in the middle of the melee, and video obtained by MLB reportedly shows the 23-year-old punching Rays infielder Evan Longoria in the back of the head, knocking off his cap.
Cabrera, who was also suspended and fined for violent and aggressive actions, again denied on Sunday that he hit a player.
"I'm going to see the video today to see what's in it," Cabrera said. "I'm insisting I did not hit him."
The players have until March 21 to officially appeal their punishments. Duncan said he spoke to Yankees general manager Brian Cashman to apprise him of his decision and said he was entrusting his situation to his agent, Barry Meister.
"My agent is a great agent," Duncan said. "There's a lot of stuff that I'm going to put his hands on so I can just come to the field and just worry about baseball. It's hard enough when you have a lot of stuff going on. I'm going to put a lot of trust in him to do what's best for me in this process."
If the suspensions are upheld after appeal, both Cabrera and Duncan could miss the first three games of the regular season, forcing the Yankees to play with 23 players for their series against the Blue Jays in New York.
Both players would then return to action on April 4 against, of all teams, Tampa Bay.
"It'd be awesome if the whole thing got overturned for everybody," Duncan said.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.