Per Mertesacker's header just before the break was enough to seal the three points at Craven Cottage.
Fulham had been reduced to ten men early on when Steve Sidwell saw red, but even a man down the home side pushed Arsenal all the way, who had Olivier Giroud sent-off in the final minutes.
But Wenger was very happy overall, and told Sky Sports: "Of course for us after the draw against Everton it was important to take the three points.
"It was a positive first half, but for some reason, and I don't know why, our game in the second-half deteriorated and our passing became sloppy. We played with less pace in our game and you have to give them credit - they are a good side and they tried like mad. They played very well today."
Wenger admits that they did not play well against the ten men and failed to take full advantage of the situation.
"It became hard, and in the second-half especially I think we played with a hand-brake," he said.
"We just wanted to keep the lead without taking any risk and had not enough penetration. When a team is down to ten men they focus on defending deep and they defended well. We did not give them enough problems today."
Wenger admitted he thought both red cards were correct. Asked if they were right, he said: "It looked like it, I spoke with Giroud and he said he slipped when he went for the ball and I don't complain about it."
Giroud's red means he will now miss three of Arsenal's last four matches and Wenger admits that is an issue.
"Unfortunately yes we have to find a solution up front for the final games, but that can happen and we have to deal with it," he said.
"The result is the most important thing now, but the best way to get the result is still to play well. I think the nerves played a part in the second-half as we did not want to be exposed and we lost our fluency.
"We have always had difficult games here and we lost here last season. But we won this season so that is a good sign. Look at Everton losing today, both teams gave everything and you could feel some players were tired."