Thomas Vermaelen's own goal gifted the visitors, who had not won at Arsenal in 25 attempts, the lead after 65 minutes.
The Belgian went on to redeem himself when nodding in from close range with seven minutes left but the Gunners could not conjure up a winner.
Wenger believed his squad had shown "a bit of mental and physical fatigue" after their exertions in the midweek victory over Borussia Dortmund which had secured safe passage into the knockout stages.
"The positives are we have shown an exceptional spirit and desire, refusal to lose the game," he said. "You could see many players were on the fringe and that we had not completely digested the Champions League game on Wednesday night.
"We needed to dig deep, the circumstances in the game went against us because the moment when Fulham scored they were not crossing halfway a lot. We scored an own goal at a moment when it was all us, earlier in the season, we could have lost this game, but we came back. It is disappointing because we dropped two points but at least it keeps our unbeaten run going."