Butler was relegated to just one snap on a special teams play in Sunday's 41-33 loss to the Philadelphia Eagles.
While the 27-year-old said he "could have changed that game" if given the chance, coach Bill Belichick said after the end of the contest and again on Monday that he had to make decisions that were best for the team.
Belichick did not go into detail on those decisions, but Rapoport reported that Butler violated a team rule related to curfew. He also said that the cornerback had a bad week of practice as he battled flu-like symptoms.
"There are several factors that led Malcolm Butler, one of the team's top defensive players, to not be on the field for the Super Bowl," Rapoport said. "Among those: he showed up a day later than teammates because he was sick. Remember he was not at Opening Night, that was a factor.
"I'm also told that during practice this week, he really struggled, had a rough week of practice. Perhaps because of illness, but maybe because of ... other things. That was one thing they had to consider in putting Eric Rowe out there instead of him.
"I'm also told there were also disciplinary issues. There was a small or minor violation of team rules that happened earlier in the week. Then there's some attitudes, frustrations as well. "
Former Pro Bowl cornerback and two-time Super Bowl champion Brandon Browner also noted on Instagram that he believes Butler violated a couple of team rules. He went on to say that he believes Belichick was showing his power with the decision.
"That (expletive) was some power trip shit, feel me? Like to prove a point," Browner wrote. "They felt like they had the quarterback to do it with. We don't need you as a cornerback. Man, you play every game of the season but the Super Bowl. I can't rock with that. That was (an expletive) call. That was (an expletive) decision. That was a power trip.
"You divide the locker room when you do that. ... You divide the locker room. Cats says they rocking with Malcolm and cats say they rocking with the coach's decision."
Belichick responded to Butler's desire to play in the Super Bowl on Monday.
"I respect Malcolm's competitiveness and I am sure that he felt like he could have helped," Belichick said on a conference call. "I am sure other players felt the same way, but in the end, we have to make the decisions that we feel are best for the football team and that is what we did, that is what I did. That's really all I can say about it."
When pushed for a further response as to why he felt it was the best approach, Belichick offered the following:
"I appreciate the question, but it would be a much longer discussion," Belichick said. "There are a lot of things that go into that. In the end, the final decision is what I said it was."
Butler had played on 97.8 percent of the defensive snaps in the regular season and all 74 snaps in the AFC Championship Game win over the Jacksonville Jaguars.
"They gave up on me," an emotional Butler told espn.com as he walked to the team bus after the game. "F--. It is what it is."
Butler was spotted near tears during the singing of the national anthem prior to the game.
Three years ago, Butler etched his place in Patriots' lore as he became the hero in Super Bowl XLIX in Arizona, when he intercepted Seattle quarterback Russell Wilson on the goal line in the closing seconds, preserving the Pats' 28-24 win over the Seahawks.
Butler, who will be an unrestricted free agent, is a former Pro Bowler. A former Eagle, Rowe, played most of the game in Butler's place and struggled, as did most defensive players in this offensive extravaganza. Rowe was a second-round pick of the Eagles in 2015, and was traded to New England a year later.
Three years ago, Butler was the fifth cornerback on New England's depth chart coming into Super Bowl XLIX but replaced Kyle Arrington, a nickel defensive back, in the third quarter. Two plays after allowing a juggling 33-yard reception to Jermaine Kearse, Butler intercepted Wilson's pass to Ricardo Lockette at the goal line with 20 seconds left to preserve New England's fourth Super Bowl title.