In a game of few clear-cut chances it was Dimitar Berbatov who made the difference with a well-executed finish in first-half stoppage time.
Jonathan Walters missed a second-half penalty for the visitors who had struggled to get into the game before the interval and are now only a point ahead of the Cottagers in the table.
The point at which Stoke should be safe is on the manager's mind, and Pulis will not accept they are certainly staying up "until we get 40 points, and we are still seven away".
"That will be the watershed and always is for me," Pulis said. "I think everyone in the league who hasn't got 40 points will be (looking over their shoulders) that is the way it is.
"The league is a relentless league and every game is a tough game as we found out again here."
Pulis also bemoaned Walters' penalty miss as a turning point in the game for his side, who coped better with Fulham after the interval.
He said: "The first half was a very, very dead game and the only bit of quality was Berbatov's. Personally I think Fulham did not cause us many problems in the second half. We needed to score the penalty but we didn't.
"If we score the penalty then it is a different game. We have been closer in away games this year and have had opportunities and chances that we haven't taken."