A deserved 3-1 win over Liverpool took Tony Pulis' side to within two matches of their all-time top-flight unbeaten record.
But while the Potters, who have never finished in the top half of the Barclays Premier League, sit eighth just five points adrift of fourth place, Walters stressed it was very much business as usual.
"We can't get too ahead of ourselves," said the Republic of Ireland international, who scored twice either side of Kenwyne Jones' header as Stoke recovered from Steven Gerrard's first-minute penalty against Liverpool.
"We've got Southampton and then (Manchester) City on New Year's Day and we have to keep going and keep our feet on the ground and as long as we do that we will be all right."
- Sports & Recreation
- Barclays Premier League
- Tony Pulis