The Blues can replace league leaders Manchester United at the top of the table on goal difference with a win at the Etihad Stadium.
"There's always a danger of losing concentration if it's not in your own hands, but now it is," Barry told the club's official website.
"To call it a second chance is probably right. It's all built up to a huge game on Monday and we're all really looking forward to it.
"When the game is that big the pressure is on both sets of players and it's probably going to be down to who handles that best."
City's last championship win came 44 years ago back in 1968.