Stoke boss Tony Pulis was disappointed his side could not convert the chances they had to put themselves "out of sight" at the Britannia Stadium.
After Potters defender Robert Huth had headed wide on the quarter-hour mark, Charlie Adam put the hosts in front in the 26th minute with a shot on the turn from close range.
Stoke continued to carve out opportunities, with captain Ryan Shawcross going closest by nodding against the bar, but were unable to add to their tally.
That made for some anxious moments for their manager, particularly towards the end as Fulham stepped up their search for an equaliser, and reflecting on the contest, 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," he added.
Sunday Indo Sport