The Switzerland international was given a straight red after a VAR review showed he had grabbed midfielder Ashley Westwood by the throat.
Xhaka had gone some way to healing his rift with supporters in the last 12 months but supporters turned on him again following the red card, as it allowed Burnley a foothold in the game.
Pierre-Emerick Aubameyang’s own goal sealed all three points for the Clarets and Mikel Arteta criticised Xhaka afterwards, claiming he had ‘cost’ his side the victory.
It’s far from Xhaka’s first misdemeanour at the club and Evra believes he should ‘offer’ to leave the club after the red card.
‘I have nothing against this player,’ Evra told SkySports.
‘But I am sorry it is time for him to say: “Do you know what guys, I have done enough here, I am hurting the fans, I am hurting my team-mates, I am hurting the manager, let me go away”.
Arsenal’s defeat means they’ve accrued just 13 points from their first 12 matches this term, which is their worst record at this stage of any Premier League campaign.
The pressure is building on Arteta and the Gunners have been drawn to face Benfica in the Europa League.
Southampton visit the Emirates on Wednesday.