The Gunners swiftly took a two-goal lead but were pegged back before the break and ultimately had to settle for a 3-3 draw.
Mikel Arteta missed a last-minute penalty to compound Wenger's misery and make it three games without a win in all competitions for Arsenal.
Wenger believes that Arsenal wasted the chance to claim three points by letting their foot off the pedal against Martin Jol's men.
He told the club's official website: "It was frustrating because we had the opportunities to win the game.
"We were caught in a bit too comfortable a position because we did the most difficult thing, we scored two goals to go 2-0 up, we were at home and yet at half-time we found ourselves at 2-2. At that moment we lacked urgency defensively.
"In the second half we gave absolutely everything and I have to give credit to the players, in the last three games what they have done physically is amazing. Even at 3-2 down we didn't give up and continued to go forward and we had the chances to win the game."
A point against Fulham leaves Arsenal languishing in 11th place in the Premier League table.