Aubameyang had the chance to seal three points for Arsenal, but he saw his 91st-minute spot-kick saved by Hugo Lloris.
Per Jack Rosser of the Evening Standard, Xhaka said: "If you take a penalty in the derby you have big balls. Not all of the players would have taken this one. So we are happy he took the penalty. If he scores he scores, if he doesn't score he doesn't score. This is football."
The midfielder added: "In this moment you have to leave the player alone. Because he has a lot to think. He was of course not that happy. But we are a team, and we win and lose together. So he was unlucky today but he helps us a lot in games so it's not something big."
He echoed a similar sentiment on social media after the match, per Football.London's Charles Watts:
As football journalist Mattias Karen noted, it was a poor effort from Aubameyang:
The penalty should have been retaken because of Jan Vertonghen's encroachment into the penalty area, though the Gunners were perhaps fortunate to have been awarded a penalty in the first place after Aubameyang appeared to go down easily as he and Davinson Sanchez contested the ball.
The penalty came after Harry Kane had cancelled out Aaron Ramsey's opener with a controversial spot-kick of his own at Wembley Stadium.
While there has been much debate about Kane being in an offside position when Christian Eriksen's free-kick into the box was taken, he was carelessly brought down by Shkodran Mustafi.
Football.London's James Benge felt the German was more to blame than Aubameyang for Arsenal's failure to win:
Alexandre Lacazette, whom the Gabon striker replaced from the bench, also bears responsibility as he failed to even hit the target when presented with a gilt-edged chance from close range.
Aubameyang has only scored twice in his last seven Premier League matches for Arsenal, but he has had a strong campaign overall with 16 goals in England's top flight.
Thanks in part to his efforts, Arsenal are just one point off the top four and four points off Spurs in third.
If he can rediscover the form he showed earlier in the campaign in the Gunners' nine remaining league matches, they'll have a fighting chance of securing a top-four finish.