The Potters capped another impressive season in the Barclays Premier League by reaching the FA Cup final and, although they lost 1-0 to Manchester City, the run will live long in the memory - not least their 5-0 semi-final victory over Bolton at Wembley.
Begovic's personal success in ousting Thomas Sorensen from the number one position meant he had to give way to the Dane on the cup run, but the positive effect was felt throughout the whole club and city.
Having been written off as relegation fodder when they achieved promotion in 2008, Stoke have continually proved people wrong, and Begovic has targeted a first top-10 finish for the 2011/12 campaign.
He said of the cup final: "It was a great experience for everybody involved in the club and that gave us a little taste of what could happen. It's something that we'll work hard to keep achieving.
"Last season was great on all fronts. Personally, breaking through and getting into the team was fantastic and seeing the success the whole team had was brilliant as well.
"So now we want to push on and have a better season this year hopefully. Your goal every year is to get better, and we're trying to get better as players, get better as a club.
"It's going well so far. It's a good challenge. Top 10 would be fantastic. It's going to take a lot of hard work."
Stoke's cup heroics combined with City's top-four finish meant the Potters qualified for Europe for the first time, drawing a plum third qualifying round tie with Hajduk Split in the Europa League.
It was another milestone for the club, who had not competed in Europe since 1974 and will try to win a continental tie for the first time in their history.
Victory over two legs and in the following play-off would earn Stoke a place in the group stages, meaning an extra six matches - something Begovic would relish.
He said: "We've got a long way to go. It's a very tough task. If we do reach the group stage it would be fantastic. I think the fans would love it. Of course it will bring more games into the season but I'm sure we'll cope with everything."
Begovic, whose family fled war-torn Bosnia when he was four, joined Stoke last January after seven years at Portsmouth.
Despite never being number one at Pompey, Begovic began to attract the attention of other Premier League clubs, and last October he finally got the chance he was looking for.
Injury to Denmark international Sorensen prompted Stoke boss Tony Pulis to turn to Begovic, and the 24-year-old has not looked back.
He knows, though, that Sorensen is far from happy sitting on the bench and he will have to continue his impressive progress if he is to stay ahead of the Dane and number three Carlo Nash.
Begovic added: "It's a good club and there's going to be competition for places everywhere. It's no different with us. I'm ready for the challenge.
"They're two great keepers and two good guys also to hang around with and train with. We try to get the best out of each other and that's what you want to have.
"I know I have to be on top of my game to keep my place and try to get better myself. I'm still learning in the game, I'm still very young, so it's a good situation to be in.
"The manager's been great. He's given me the chance to play in the team and of course I owe him a lot. He's given me the platform to play, to learn and to get better, and the whole staff have been fantastic."
Source: Team Talk
Source: Team Talk