"I feel stronger with every game but the thing that was missing was a goal. I've now got one which will really help my confidence."
Jonatan Johansson also ended a long barren spell - his two goals were his first since February. Stuart added: "Not only did he score but he worked really hard for the side."
Chris Coleman described Fulham's performance as the worst since he became manager, while goalkeeper Edwin van der Sar was so angry during the game that he kicked his own post.
The Dutchman said: "We did not work hard enough, that was the big difference. "Now we have two weeks before we can make up for it. It would be better to be playing next week."
Both sides suffered injury blows. Charlton's Claus Jensen limped off with a knee problem and Fulham striker Barry Hayles twisted his ankle.