After seeing skipper Vincent Kompany dismissed for a two-footed tackle against Manchester United last weekend, Liverpool's Glen Johnson escaped punishment after a similar lunge in the midweek tie with City at Eastlands.
Barry has insisted that the club's anger is not aimed at Johnson, but at what they see as a sense of injustice.
"Yes, I think there is beginning to be a sense of injustice, of course, after nothing was done about the Johnson tackle," Barry told The Mirror.
"Once the decision has been made and we know Vinny's going to get a four-game ban, our fans are going to want to see action every time there is a similar sort of tackle."
City return to domestic action against Wigan Athletic on Monday evening.