The former Liverpool midfielder says the club are aiming as high as possible, but won't take anything for granted.
The Potters are currently 10th in the table, just five points off Tottenham in 7th position and competing with several clubs for a potential Europa League finish come the end of the campaign.
Their form of late hasn’t been the best, though, having lost 4-1 to both Manchester City and Blackburn in the FA Cup the week before, although they were doing well before those results.
They take on struggling Everton in the Premier League on Wednesday evening, and Adam says nobody at the club is getting complacent.
“It’s going well at Stoke at the moment although with 11 tough games to go nobody’s taking anything for granted,” the midfielder wrote on his Kicca account.
“Our aim is to finish in the top ten this season and then consistently repeat this over the next few years, building each time on the previous season. We’re determined to be a top half club this season and every season. Although, in truth, the more likely route into Europe is through the cups.”
The former Liverpool midfielder has also praised manager Mark Hughes for the club’s upturn in fortunes, saying his experience and smart buys have pushed the club on.
The Welshman replaced Tony Pulis at the Britannia last season and went about changing the club’s style, with his team playing a more technical brand of football to the long-ball football tag that was often thrown upon Pulis’ sides.
Aside from the manager, Adam thinks that the players must come in for some of the credit as well; saying the core of long-term servants have been supplemented well in the transfer market.
“What’s the secret behind our achievements so far? It’s simple,” added Adam.
“We have a good group of players, the core of which have been at the club for a good period of time, then supplemented by some smart buys. We have the right players at the club and a manager who was a top player and very experienced.”