Tottenham broke the deadlock early in the first half after mistakes from Sokratis Papastathopoulos and Bernd Leno led to Christian Eriksen’s opening goal.
Arsenal’s poor start was compounded when Xhaka’s reckless challenge on Son Heung-min resulted in a 40th-minute penalty, which Harry Kane dispatched without any problems.
The Gunners battled back to rescue a point thanks to goals from Alexandre Lacazette and Pierre-Emerick Aubameyang either side of half-time at The Emirates.
Arsenal find themselves five points behind Premier League leaders Liverpool FC after Unai Emery’s men dropped points for the second successive top-flight game.
Xhaka took to Instagram to send a message to Arsenal supporters following his error in the derby clash.
Xhaka wrote on the social media site: “Thanks for the amazing support inside the Emirates 👏 We showed a lot of character and you helped us to come back into the game. For the penalty I made a mistake – I’m of course angry about it but I will never give up! @arsenal #GX34”
Arsenal will return to Premier League action with a trip to Watford on Sunday 15 September after the international break.
The Gunners have collected seven points from their opening four Premier League games to make a solid start to the 2019-20 season.
The north London side are hoping to qualify for the Champions League this season after missing out on a top-four finish in three previous campaigns under Arsene Wenger and Emery.
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