Sheffield was hit by a pitch from Carmona last Friday night in Cleveland. Moments later, the designated hitter charged the mound from first base, starting a bench-clearing scrap.
"I've been in a lot of brawls, being a peacemaker, and when someone's back is to you, you pull them away -- that's what you are supposed to do," said Sheffield, who will not appeal.
"You don't take cheap shots, and that's what happened. I take that personally, and when I find out who it was, they are going to have to deal with me," he said.
Sheffield chose not to give any details about what he meant when he said the Cleveland players would have to "deal" with him.
"I'm not going to get here and talk about what I'm going to do," he said. "I'm just going to do what I'm going to do, and if I challenge someone, I'm going to do it to their face. I don't want it to be a surprise."
Carmona and Martinez will appeal their penalties, which were to have started Monday night when the Indians played at Boston. It was not immediately known whether Cabrera would appeal; his suspension was to begin Thursday.
Sheffield will start sitting out Monday night when Kansas City visits Detroit. He needs three homers to reach 500, but said he didn't consider appealing to give himself a better chance to do it this year.
"I didn't even think about that," he said. "We're not going to be in the playoffs, so it is best to get it over and have a clean slate next year."
The Indians and Tigers are both finishing up disappointing seasons and do not play each other again this year. Sheffield said he wasn't worried that his apparent threats might draw further discipline.
"I don't care about what the league thinks or what they do," he said. "I've got enough money to pay any fine they've got. Trust me."
A day after the brawl, Sheffield seemed particularly peeved at Martinez, who pointed at the Tigers veteran as he was being pulled from the pile.
"He hasn't done anything in this game," Sheffield said then. "He's had a couple of [good] years. When you have a catcher chirping like he's something special ... like he's done something. He hasn't done anything."
Sheffield was in Detroit's original lineup Monday night. Manager Jim Leyland wasn't surprised that he had to change his plans.
"I thought I might have to do this," he said while tearing up his lineup card.
Leyland declined further comment, since he was not managing the Tigers during Friday's game because he'd recently been suspended three games for "inappropriate conduct" directed at umpires.
"I don't think it would be ethical for me to comment, since I wasn't involved in the game," Leyland said.