Roberto Mancini's side were favourites to take the trophy for much of the season but a slump in form allowed Manchester United to put an eight-point gap between the teams in March.
However, a resurgence in form alongside a stutter in the Red Devils’ results means that Monday’s match at the Etihad Stadium could help decide which half of Manchester will rule come May.
“You've always got to hope,” Barry admitted to the club’s official website. “There's always a danger of losing concentration if it's not in your own hands, but now it is.
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“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.
“There's probably been less pressure on us in the last few games.
“I don't think you can get away from the size of the game against United and the pressure on the team.
“It's not really an excuse. 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.”
Barry admitted that City's final two games after United are far from simple - a trip to Newcastle United, who are chasing third spot, and hosting relegation-threatened QPR on the final day of the season.
“I think initially, because the derby is the next game, it is a must-win for us,” the midfielder continued.
“Then you have to look after the games still to come. If we get a positive result against United that certainly is not the end of it.
“Newcastle and QPR have got so much to play for themselves.
“People are speaking of this as maybe being the biggest game in Premier League history and, on a personal level, it's a massive game for me to be playing in.”
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Barry added that the topsy-turvy nature of the English top flight, with downs as well as ups for City over the season, is a factor which he enjoys.
“We can look further back in the season to when we were clear and people were maybe thinking it was over for United, but they came back strongly," he observed.
“It's just the Premier League and the way things are. It's such a long season and so much can happen.
“I've really enjoyed this season. I've had a great run of games and it's fantastic that we're still challenging for the title.
“It goes without saying we'll be giving our all to try and take advantage of the situation, but as I say, we have three huge games left so we need to take one game at a time.”