Roberto Mancini's side sit on level points with Manchester United at the top of the table and the England international believes that his teammates need to be willing to grind out results in order to keep up the pressure.
"This is the time when people will really be watching us, to see how we respond to this sticky patch," said Barry. "If it means going there, not playing great football and battling to get a victory, we might have to do that.
"You can't dominate the whole league playing fantastic football and winning every game easily. Sometimes you have to battle and scrape a result in the last minute.
"Wigan is set up for that sort of game. Everyone in the dressing room has to roll up their sleeves and be ready to do it."
City travel to the DW Stadium for tonight's clash.