The highly-rated Potters shot-stopper is eyeing three points against champions-elect Manchester United at the Britannia Stadium on Sunday, despite the club sitting just above the drop zone.
But the 25-year-old Bosnian feels City are capable of looking beyond the 40-point mark with games against QPR and Norwich to come in April.
"It's just like everything is going against us at the moment," he said.
"We were world beaters at Christmas. Now we're getting hit with top-corner screamers, penalties, this-way-or-that-way decisions. It's unbelievable the kind of run we're on.
"You just have to keep going, stand up and keep fighting. We realise we're in a dogfight. But we're setting our sights high, looking at 40 points, and beyond, to make sure."
Begovic's performances this season have seen him linked with a big-money move elsewhere at the end of the season, with Sunday's opponents among those reportedly interested.
Stoke boss Tony Pulis said: "It doesn't surprise me that there are links with the top clubs. It's been a great season for him. He can only get better and better."