Barry believes that the tag of reigning champions gives teams an extra incentive to try to claim City's scalp.
He told the Daily Star: "The start of the season is completely different to last year, but this season is what being champions is all about.
"You're going to find it tougher because teamswant to beat you that little bit more.
"And this is what we're finding out."
City have also failed to make a strong start in their second season in the Champions League, taking just one point from their opening three group matches.