Roberto Mancini's men face a crunch clash at home to high-flying Tottenham on Sunday afternoon with the visitors seeking to gain revenge for their 5-1 hammering at White Hart Lane back in August.
However, the Blues are unbeaten at the Etihad Stadium in the league and have recorded 10 straight wins, while Harry Redknapp has led Spurs to third place in the table after just one defeat in the last 19 outings.
And former Aston Villa star Barry believes the game against the side from North London could prove crucial in the championship chase.
"There's big pressure on us now," the 30-year-old told the Daily Mirror. "It's a vital part of the season. There are still a lot of games left, but this period now, after a little sticky patch, is important.
"The game coming up against Spurs is a huge one in the title race. The lads aren't thinking about the money the club has spent at all - they're thinking about winning the league.
"That's the pressure - trying to win the title. Managers can see when pressure is affecting players, and that's where they must make their decisions. Pressure can affect some players more than others.
"We're going into games now, knowing they're all big and that there's so much at stake.
"Earlier in the season the players were playing a lot more freely. But at this stage it's all about getting three points and sometimes the football may not be as pretty."
Barry also expects the war of words between the title contenders to hot up as the season draws to a close, although he does not think Mancini, who led Inter Milan to three successive Serie A titles, to get too flustered by the experience of Sir Alex Ferguson and Harry Redknapp.
"In terms of mind games, there have been opportunities when our manager could have had a little bite, but he's resisted it and not really reacted," continued Barry.
"I think that's definitely the right thing to do. The route the manager has gone down has certainly helped the players.
"He's not added any more pressure on us before the games and the players feel very comfortable that he knows what he is doing.
"The manager is in charge of what you do, so if you see him getting involved in other things away from the pitch, it's going to make everyone unsettled.
"Inside, the manager probably feels the pressure a bit more if the results aren't going right.
"But judging by the way he's approached it and spoken to us, he's certainly not showing any signs that he's under any more pressure."