The club have made an impressive start to the season and currently occupy fifth place in the league, but Begovic wants to make sure that the they do not endure another poor season.
"We just want to improve every year, we had a disappointing end to last season and we don't want that to happen again," Begovic told talkSPORT "We want to kick on and push the club forward.
"The work that we've done with the new gaffer, Mark Hughes, has been brilliant so far. From the very first day of pre-season everyone has really bought into his ideas and as long as we keep improving every day, work hard and get better as a team, we can surpass all our goals this year.
"With the way that we've invested and the players that we have, it's time for this club to push for the top ten. We don't want to take safety for granted so we have to reach the 40-point level first, as many other teams do and we'll kick on from there but we really want to push for the top ten and start to establish ourselves a bit more."
Begovic joined Stoke from Portsmouth in 2010 for a fee of £3.25m.