The Spaniard missed a penalty with the last kick of the match to leave the London rivals all square after a pulsating match at the Emirates.
Arsenal allowed an early two-goal lead to slip and trailed in the second half before Olivier Giroud equalised late on.
Wenger admitted that he is growing increasingly frustrated with his side but was adamant that Arteta should not shoulder any extra blame for his penalty miss.
He told the club's official website: "Of course it is frustrating because we had chances to win the game. You cannot blame Arteta for that [penalty], it is part of the game.
"Santi Cazorla is second on the list [of penalty takers], the number one is Arteta.
"I don't think there is [self-doubt]. Some players were a bit jaded before the game and Fulham are good going forward."
Two dropped points against the Cottagers leaves Arsenal in seventh place in the Premier League, four points behind Everton in fourth place.