Stoke have been one of the most impressive teams in the top tier this season, but Adam feels it is unrealistic that they will be able to break into the top six any time soon.
The Scottish midfielder, instead, thinks that they should be competing in their very own mini league - and he wants to move ahead of the likes of Southampton, Swansea City and Everton.
“You’ve got the likes of Chelsea, Man City, Arsenal, Liverpool, Manchester United and Tottenham all there," Adam said.
“To catch those teams, even Liverpool and Tottenham who are fifth and sixth, with the amount of money they’re spending, it will be difficult.
“I think you have to be realistic, there’s another league for us really, competing with Southampton, Swansea and Everton, they’re the type of clubs we’ve got to be looking at and trying to challenge.”
At the moment Stoke are in ninth position in the Premier League table, which is behind both Southampton and Swansea, but ahead of Everton.
It has been a very impressive season for the Potters, who don't seem to have received the credit they deserve for their performances.
Stoke have progressed hugely under the stewardship of Mark Hughes and they are now a side which many teams in England will try to emulate.
Stoke have become a stable Premier League club and Adam is clearly looking to keep the side moving forward in the future with his aims.