Bath's Barbeary handed three-week suspension after red card
The number eight got a red card after two yellows - for a high tackle on Max Spring and a forearm challenge on Nolann Le Garrec - and England coach Steve Borthwick said the disciplinary situation was a factor in his omission from the squad.
An independent Disciplinary Committee upheld the first citing for a dangerous tackle in the neck area but dismissed the second as the match officials were correct in issuing a yellow card as the player's actions did not warrant a red.
Barbeary was excluded from England's Six Nations squad on Wednesday but Borthwick did not rule out a return in the future.
"We need some certainty in the squad but if he continues to go the way he is then he'll be a big part of the England team and he should be," Borthwick said.
Due to Barbeary's acceptance of the charge and his good disciplinary record, the committee reduced the sanction by the maximum of 50% before imposing the three-week suspension.