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 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."
That was a sentiment echoed by Pulis, who for all his delight at beating Liverpool at the Britannia Stadium for a third time in five matches, stressed the importance of remaining focused.
"The first thing I said after the game was that it was a fantastic performance, and you couldn't take that away from us, but our toughest game this week will be Southampton because of the expectations of everyone around the place," he said.
"Forty points (is the target) as quick as we can and then we will look at it - that's the way it has always been at this club."
Walters' goals were all the more sweeter as he was a boyhood Everton fan.
But he also paid tribute to Jones, who was impressive throughout and provided the flick-on for Walters' impressive volleyed second.
"All my family will have been cheering, it is nice to score against Liverpool being a blue," he said.
"Whoever scores it doesn't matter, it is a team effort. As long as we spread the goals throughout the team and we keep winning we will be happy.
"Kenwyne has done excellently. He is such a threat in the air and holding it up and when he's on it he is really on it.
"Kenwyne or (Peter) Crouch, whoever is playing, are such a handful up front and it is nice to have two good players like that."
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