Arsenal’s insistence on trying to play out from the back went horribly wrong in the 39th minute when Xhaka’s attempted pass in his own box went in off Chris Wood, cancelling out Pierre-Emerick Aubameyang’s opener for the visitors.
Xhaka’s error cost the Gunners two points, with Mikel Arteta’s men sitting 10th on the table with 38 points from 27 matches played.
"I hold my hands up for their goal and I'm sorry for the mistake," the Switzerland international, who was handed and then stripped off the Arsenal captaincy last season wrote on his official Instagram page after the game.
"That's football and right now I feel just as frustrated as all of you."
Arteta refused to criticise Xhaka after the match and urged his side to perfect the art of playing out from the back.
"We are talking about [cheap goals] all the time and just trying to nullify anything that we give to the opponent," he said.
"In the last few weeks, we have done that. We have to improve that individually, as in the end we have to make decisions on the pitch and it looks easy from the outside.
"It's not that easy away from home, but if someone makes a mistake because they're playing the way we want to play, I will always support them. If someone is hiding and doesn't want to play and then makes a mistake, I'm not going to have that."