The Staffordshire outfit have now taken nine points from a possible nine after also beating Birmingham and Liverpool, marking quite a turnaround from their four consecutive league defeats which preceded that.
"We have been on a bad run of four straight defeats in the Premier League and now we have three straight wins, which is the first time this club has done that in the Premier League," Pulis said.
"It is a great achievement by the players, but as I have said, whether you are losing or winning, I think it is important the manager stays as level as he possibly can.
"I'll allow the supporters to get down and despondent or happy and getting carried away."
Pulis was delighted to see Walters score a brace to cap the week in which the striker had made his debut for the Republic of Ireland.
"It is brilliant," said Pulis. "I spoke to (assistant manager) Dave Kemp before the game and I really wanted to get Jon on after he had made his debut for the Republic this week.
"It has given him such a boost and you just want to get him on there."
Source: PA
Source: PA