After Potters defender Robert Huth had headed wide on the quarter-hour mark, Charlie Adam scored the crucial goal in the 26th minute, before captain Ryan Shawcross nodded against the bar.
The hosts were dominant but had to endure a few late flutters as Fulham poured forward in search of an equaliser.
Pulis said: "I'm really disappointed we have not won the game by more goals.
"Even just looking at the first half, if you look at the chances, Robert has missed a point-blank header from a corner and Ryan hits the bar when he is almost under the goal.
"There were some great opportunities and in the second half we had more. Then in the last few minutes, you are starting to scramble.
"We had so many chances and you get a little bit uptight because you know one mistake could have cost us the game - a game that we should have been out of sight in."