Swinney said the players had violated a 1 a.m. curfew Wednesday night, the team's first in Nashville last week as it prepared for the game.
"The first night here I gave them a little later curfew," Swinney said Saturday, according to The Greenville (S.C.) News. "Plenty of time to go out, have a good time and get back."
Barry and Johnson are seniors, but Cumbie, a junior, was a key piece as part of the regular rotation in the Tigers' defensive line.
Cumbie recorded 60 tackles and two sacks this season. Moore had 19 tackles with two sacks.
"There [are] consequences for every action," Swinney said. "They weren't out doing anything illegal or anything. Just late, and the consequences are they won't play."
Defeats in its final two games put a damper on Clemson's first full season under Swinney, who replaced Tommy Bowden on Oct. 13, 2008, and guided the Tigers in the final seven games last season.
Clemson and Kentucky had their bowl sights set higher than a trip to Nashville. Close late-season losses, however, relegated them to a Music City Bowl matchup for the second time in four years.
The Tigers, led by ACC Player of the Year C.J. Spiller, have lost three straight bowl games, while the Wildcats have won three in a row.
Clemson (8-5) reached the ACC championship game against then-No. 10 Georgia Tech on Dec. 5, with the school's first league title since 1991 and a spot in the FedEx Orange Bowl at stake. Despite 233 yards rushing and four touchdowns from Spiller, the Tigers lost 39-34 on Jonathan Dwyer's 15-yard TD run with 1:20 remaining.
"We've come a long way in one year," Swinney said. "This is where Clemson is supposed to be. This is our standard. This is our expectation. So hopefully we can grow from this."
Left with its third trip to Nashville in the past four years, Kentucky (7-5) settled for the Music City Bowl after a 30-24 overtime loss to Tennessee on Nov. 28.
"We had our sights higher. Still, it'll be a great game," said Kentucky receiver Randall Cobb, a Tennessee native.
Information from STATS LLC was used in this report.