The Potters, beaten only three times in their first 20 Premier League fixtures this season, have now suffered six defeats in the eight top-flight matches that have followed.
All that has left them in 11th place on 33 points, and Pulis wants to see his players rouse themselves in their final 10 games for a strong finish to the campaign.
After the West Ham reverse - only the second time Stoke have been beaten at home in the league this term - Pulis said: "We have gone a little bit flat and we have to shake ourselves out of it, without a question of a doubt.
"We need to get over the line - get 40 points.
"It is only our second home defeat and that is most probably as disappointing as anything, because our home form has been excellent this year."
Jack Collison netted the winner on Saturday, collecting a through-ball from his fellow substitute Ricardo Vaz Te, turning and firing a shot beyond Asmir Begovic in first-half stoppage time.
West Ham had already gone close, with James Collins sending a header on to the bar, and were the side to create more clear chances throughout a game of few, although they only emerged with the victory having survived a couple of late scares.
A volley from Stoke substitute Adam crashed against the goalframe in stoppage time at the end of the match, and the hosts' protests that Hammers defender Guy Demel had deliberately handled in the area were then waved away by referee Jonathan Moss.
Ultimately, Pulis' men did not produce enough on the day, something acknowledged by Adam - although the Scotland midfielder has stressed that there should not be too much doom and gloom in the Potters camp.
"We huffed and we puffed for 90 minutes, but sadly the quality or that cutting edge just wasn't there, and I suppose in the end it just wasn't our day," said Adam, quoted on Stoke's official website.
"It's disappointing, of course it is - nobody wants to lose games. But there is a lot of positives to take from the season so far, there is no doubt about that."
He added: "We have plenty of games to go and we are in a good position in the league, so let's not get too carried away.
"There are 30 points to play for and we will be doing everything we can to get as many of them as possible."
The result moved West Ham up to 12th, level on points with Stoke, and their boss Sam Allardyce believes five more points will be enough to ensure his team - promoted from the Championship last year - avoid relegation.
The Hammers, now nine points clear of the drop zone, are another side who started the season fairly well before hitting a slump, and Allardyce feels the London outfit's efforts overall this term have been commendable.
"We have finally broken the away form scenario in terms of results, and that is our third away win," he said.
"We have not got enough draws away from home when we should have got them and ended up losing them.
"So we put ourselves under enormous pressure, but with the great start we had to the season, our lowest position in the table in the entire season was before this match (14th).
"So when you look at it over 27, 28 games, for your first season (back in the Premier League), even though you are feeling the pressure because you are slipping down, it is not bad is it?"
Allardyce, who was appointed as West Ham manager in the summer of 2011, is out of contract at the end of the season.
Asked about his future, he said: "Staying in the Premier League is everything about my future - that is all I have had to say over the last few weeks.
"It is where I want to be and where I want to apply my skills because I like the euphoria, excitement and pressure that it brings.
"It is the best league in the world and the most entertaining, so plying your trade in it is what you want to do."
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