It looked like being a comfortable afternoon for the Gunners as they raced into a two-goal lead, but the Dimitar Berbatov-inspired Cottagers turned the tie on its head to lead 3-2 at one stage in the second half.
Arsenal came again to snatch a share of the spoils, and were left cursing their luck in the dying seconds as Mikel Arteta saw a stoppage-time penalty saved by Mark Schwarzer.
Asked if Fulham deserved to take something from the game they offered a lot to, Wenger told Sky Sports: "Deserved is very difficult to measure. You have the possibility to win the game and we didn't take that.
"We were 2-0 up and gave two goals away. After that we showed fantastic spirit, but I believe we have not shown enough urgency in our defending at 2-0 up. Then, in the second half, we have done great and are unlucky in missing a penalty.
"We had plenty of chances. I felt that the team would continue to fight and not give up.
"The spirit was absolutely fantastic on both sides, it was a good football game. But you want the edge going for you, that didn't happen today, but it was a good game."
There was some debate as to whether Arsenal should have been awarded their last-gasp spot-kick, with Sascha Riether pulled up for a questionable handball.
Pressed on whether he thought the awarding of a penalty was the right call, having seen a similar decision go against his side at Manchester United last weekend, Wenger said: "I don't think so, no."