The manager is aware of the improvements made by Premier League side but wants his players to keep working hard.
Stoke's Tony Pulis focused on managing expectations
Stoke will begin this Premier League season with the same aim they have had at the start of the previous three - to stay in the top flight.
Since their arrival in English football's top tier in 2008, Stoke have gone from relegation favourites to a role model for promoted clubs.
Last season was the best yet, with a comfortable 13th-placed finish and a superb run to the FA Cup final, which brought with it European football.
Stoke have already made their mark in the Europa League, beating Hajduk Split over two legs to register the club's first ever victory in a European tie.
All this has been achieved under the shrewd guidance of Tony Pulis, the manager, and he is determined there will be no complacency as they prepare for their home opener against Chelsea.
"I think we have to be a little bit careful," said Pulis. "The expectation levels go through the roof.
"We've had a fantastic run of success. It's been an upwards curve now for nearly five years, and that's very unusual at any football club, that you keep bettering what you've done year after year.
"I think the great thing about the football club is the supporters have enjoyed it so much, but they remember what it's like in the Championship. They understand that our priority is to stay in the Premier League.
"Managing expectations at football clubs now is almost as difficult as managing the players on the pitch, but you learn and you have to get on with it."
There will be no opportunity for Stoke to ease themselves into the season gently, with Sunday's clash followed by home games against Liverpool and Manchester United, and trips to Norwich City, West Bromwich Albion and Sunderland.
Pulis said: "Our home form has been very important to the success we've had over the three years we've been in the Premier League, and to start with Chelsea, Liverpool and Manchester United as our first three home games, it's going to be really tough."