The Gunners dominated possession and had 12 shots but were unable to seriously threaten Kasper Schmeichel's goal.
Jamie Vardy popped up late to score the winner, and Xhaka was annoyed with the loss.
"It was a big chance to go higher, we wanted to win but in the end we lost. Leicester had nothing other than their goal, we had some chances in the first half and it is difficult to take the words so close after the game.
"We did some mistakes, if you make mistakes and if you do at this level you get punished. Mistakes are part of football, we have to analyse it, look forward, take the next step on Thursday then got to Old Trafford to get something."