Last season the club played in Europe for the first time since 1974-75, and Begovic thinks they should be aiming to make that more of a regular occurrence.
The Bosnia and Herzegovina international claims the club have already come up with a plan that gives them a good chance of a successful future, while he also feels Stoke should be aiming to emulate Newcastle United’s season.
|17/10||Stoke are 17/10 with Sportingbet to beat Reading on the opening day of the Premier League season.|
"We're desperate for the club to push on and I think there is a lot of room to grow in many respects," Begovic told BBC Radio Stoke.
"The main thing for the club, and what's happening really, is that they've tried to put plans in place for the club to be successful long term, and that's very important
"Newcastle have been a kind of a sleeping giant really, if you think about where the club was 10-odd years ago and the levels they were competing at, so it's no surprise they can reach those levels.
"For us, being in Europe has taken us into unexplored territory, so we're starting to scratch the surface and see where we can go from there."