The 27-year-old joined Stoke from Ipswich in a £2.75million deal in the summer.
Walters scored the winner against Blackburn on Saturday.
“It was a great move, a great ball through and I managed to get on the end of it and slot it in,” Walters told Sky Sports.
“It’s my first league goal for the club and I’ll keep plugging away every game.
“I’ve settled in nicely, I work hard every game and you’re expected to do that in this team, everyone works for each other.
“We’re on a great run of form and it’s good to get three points heading into the [international] break.”
