The goalkeeper believed Stoke are capable of breaking into the top ten next season.
Begovic told the Stoke website: "To reach an FA Cup Final was absolutely fantastic for the Club, and to stay up was also good achievement for us, especially considering that this was arguably the toughest Premier League for a long, long time.
"It would have been nice to have ended the season in the top ten, but unfortunately that wasn't to be. It gives us another target for next season though. We feel we are good enough to get into the top half of the league, and with maybe one or two new additions, who knows where we can go."