The Potters headed for the north-east after launching their Europa League group stage campaign with a creditable 1-1 draw in Dynamo Kiev, but misfired badly as the Black Cats secured their first win of the season.
City will have little time to reflect on a disappointing day as they begin preparations for Tuesday night's Carling Cup third-round clash with Tottenham before Saturday's visit of in-form Manchester United to the Britannia Stadium
However, Pulis is confident they will bounce back.
He said: "We have had six years of growth, of success at this football club, and it's what we have achieved.
"We have worked very, very hard to achieve this and we have to embrace and enjoy it.
"We play Tottenham on Tuesday and then we play Manchester United, two magnificent, famous football clubs in England.
"This is a great era for Stoke City and it's something we have to cope with an enjoy and relish.
"We have been punched on the chin - now we have got to get up and make sure we are ready to go for the next two games.
"You do that in football. It doesn't always run for you. It goes for you sometimes, it doesn't other times, and you have to take it in your stride and move on.
"Fingers crossed, that's what we will do."
The points were effectively banked within 28 first-half minutes as the home side, who had scored just twice this season before kick-off, finally found their touch in front of goal.
They were aided in no small part by an uncharacteristically generous Stoke defence with keeper Asmir Begovic spilling Titus Bramble's fifth-minute shot over the line before Jonathan Woodgate headed David Vaughan's cross into his own net six minutes later.
Simon Mignolet was called upon to make a rare save when he clawed away Marc Wilson's 16th-minute free-kick, but Craig Gardner's deflected shot made it 3-0 17 minutes before the break and Sebastian Larsson's delicious free-kick 13 minutes after the restart wrapped up a comprehensive win.
Pulis said: "Goals change games. The first goal was a messy goal for us, and Woody scoring an own goal and then the third goal was a deflected shot - it ran for Sunderland and they fully deserved their victory."
A relieved Steve Bruce asked assistant Eric Black to conduct the post-match press conference, and he too had a challenge for his club's players.
Black said: "You are only as good as your last game and tonight, everybody will be happy.
"We have to go out and perform again and ensure we send them home happy more often than not.
"The players have achieved it, they are the ones who got the result and let's hope they can maintain that level of performances."