Stoke have established themselves as a solid Premier League team since winning promotion in 2008, never being embroiled in a relegation battle and even reaching Europe.
However, a 14th-place finish for the Potters last season was greeted with discontent amongst some fans, and Pulis is keen to ensure that hopes don't get too high.
"It's been a great four or five years, it's very difficult to keep giving and giving and giving so we have to be careful we don't get blase about it and that people don't expect too much. Gradually we're putting things into place that this football club could never have dreamed of and we mustn't get too greedy. Staying in the Premier League is our target," said Pulis.
"That will always remain the case because if that happens then we generate the income the football club needs to reinvest. The big test this year will be our home support and how much the supporters get behind us. They've been absolutely wonderful, so we don't need them to get complacent.
"I think they have a responsibility the same as us to really be on the edge, because you need to be on the edge week in, week out. We do well because of our supporters at home."
Stoke begin their fifth season in the top flight with an away trip to Reading tomorrow.