Since their arrival in the Premier League in 2008, the Potters 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 boss Tony Pulis, and he is determined there will be no complacency as they prepare for Sunday's opener against Chelsea at the Britannia Stadium.
"I think we have to be a little bit careful," said the Welshman. "The expectation levels go through the roof.
"We've had a fantastic run of success. It's been an upward 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 - that will always be the case.
"Yes, we're looking to push on but there are some fantastic clubs and fantastic teams that we have to compete against.
"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 certainly be no opportunity for the Potters to ease themselves into the season gently, with Sunday's clash followed by home games against Liverpool and Manchester United and trips to Norwich, West Brom 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.
"But we understand that, and we understand that being in the Premier League you have highs and lows.
"This is probably the hardest run of fixtures we've had to start with but we're prepared for it, we'll give it a good go and we hope to give Chelsea a really good game on Sunday."
Sunday's clash will be a Premier League debut for new Chelsea boss Andre Villas-Boas, who left Porto for Stamford Bridge this summer.
The 33-year-old has followed in the footsteps of former mentor Jose Mourinho, and Pulis sees no reason why the Portuguese cannot achieve similarly big things.
The Stoke boss said: "He's a good coach, obviously he did very well at Porto. He's got great players, he's going into a great football club and he's got every chance of being successful."
Villas-Boas is guaranteed a noisy welcome to the English game from the famously passionate Stoke fans, who are getting behind their club in greater numbers than ever before.
Pulis added: "I think we're very close to having every home game sold out, which is a fantastic achievement by everybody connected to the football club.
"The buzz around the city is fabulous. What we've got to do is make sure we give them something to cheer about and they remain excited about what we're trying to achieve."