Xhaka cupped his ears to the home fans, who mockingly cheered his substitution during Monday's (AEDT) 2-2 draw in the Premier League, then removed his shirt before walking straight down the tunnel.
Head coach Unai Emery said on Tuesday that the 27-year-old midfielder should say sorry for the way he reacted while leaving the pitch at Emirates Stadium, while a number of former Arsenal players have called for him to be stripped of the captaincy.
In a statement released on Arsenal's official Twitter account, Xhaka apologised for any disrespect conveyed by his actions as he revealed the personal abuse that has been aimed his way.
"After taking some time to reflect on what happened on Sunday afternoon, I would like to give you an explanation rather than just a quick response," he said.
"The scenes that took place around my substitution have moved me deeply.
"I love this club and always give 100 per cent on and off the pitch.
"My feeling of not being understood by fans, and repeated abusive comments at matches and in social media over the last weeks and months have hurt me deeply.
"People have said things like: 'we will break your legs', 'kill your wife' and 'wish that your daughter gets cancer'.
"That has stirred me up and I reached boiling point when I felt the rejection in the stadium on Sunday.
"In this situation, I let myself be carried away and reacted in a way that disrespected the group of fans that support our club, our team and myself with positive energy.
"That has not been my intention and I'm sorry if that's what people thought.
"My wish is that we get back to a place of mutual respect, remembering why we fell in love with this game in the first place.
"Let's move forward positively together."
Xhaka was not part of Arsenal's squad for Thursday's (AEDT) Carabao Cup clash with Liverpool - a game the Gunners lost on penalties to exit the competition after a remarkable 5-5 draw - but was involved in training on Thursday ahead of this weekend's home match with Wolves.