Stoke City’s Peter Crouch scored a stunning volley to hand Tony Pulis’ side a 59th-minute lead before Yaya Touré netted from long range to rescue a point for title chasing City.
The result leaves City top of the table and ahead of Manchester United on goal difference, but the defending champions have a game in hand and play Fulham at Old Trafford on Monday.
“We’ve come back and got a point which keeps us within touching distance,” Barry told City’s website.
“It’s important that we keep it at no more than the three points when we do play Manchester United.
“That’s got to be our aim from now until then. It’s going to be tough but we’re confident we can do it.
“We can’t be relying on other teams, it’s down to us. We’ve got try and win all our games now until the end of the season – that’s our target.
“It’s going to be really tough but while it’s in our own hands it’s still possible.”
Barry admitted that playing at the Britannia stadium is one of the toughest trips in the league, and the England midfielder offered his support for Joe Hart, insisting the City goalkeeper was powerless to stop Crouch’s opener.
“The game was exactly how we expected,” he added. “I think that’s our third 1-1 in a row here in the league. So it was a tough battle as we expected.
“You’ve got to hold your hands up, it was an unstoppable strike. Joe Hart’s is obviously disappointed he conceded. But there’s nothing you can do about it. It should be goal of the season.”
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