Thomas Vermaelen's own goal gifted the visitors, who had not won at Arsenal in 25 attempts, the lead on 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. 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."
He added: "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."
The Gunners boss, though, insisted their European game should not be used as an excuse.
He said: "We gave a lot on Wednesday night, and it is a short amount of time to play again. But it is not an excuse, it is an explanation. We want to be in the Champions League, so we can not cry when we are tired. Our challenge is to win these types of games even when we are tired."
Fulham may have failed to improve their terrible away form with a rare win, but Cottagers boss Martin Jol feels his team can still take a lot of credit from their battling display.
He said: "A draw for us is a satisfying result. In the first half, we had 50/50 possession, with seven attempts on goal. But we could not play our football in the last 15 minutes. We tried to pass it and get it to the front players, but to get three points, you have to do a bit more."
Jol added: "Arsenal had played a difficult game in the Champions League this week, but you still have to work hard against them, because they have a winning mentality and showed that in the second half when they were 1-0 down, they did everything to score. But with their form over the past six weeks, a draw is pleasing for us."