Arsenal started on the front foot but could not find the opener despite their territorial advantage over the visitors.
France striker Alexandre Lacazette had a header ruled out for offside and he and his team-mate Pierre-Emerick Aubameyang passed up a host of first-half opportunities to put the hosts ahead.
The game was heading for a stalemate before Jamie Vardy delivered a sucker-punch to condemn the Gunners to their third league defeat of the season.
Speaking to the media after the game, Arteta admitted he was disappointed with the result as he thinks the game could have been won in the first half if not for his side’s profligacy and has urged Arsenal to improve.
“I’m really disappointed, we had it in our hands in the first half and I don’t know how the hell the goal was disallowed,” the Spaniard said.
"They caught us with space at the back and in that moment we lost the game.
"It is difficult to create spaces with 10 men behind the ball, but we should have finished the game better. When it comes to those moments you can’t give away chances at the back.
"We still had some moments after the goal but gaveaway too many free kicks. The effort that the boys put in, and the pressure the Leicester team put you under, it’s not an easy thing to do but we have to improve."
Next up for Arsenal and Arteta is a home game against Dundalk in the Europa League group stage before a visit to Old Trafford to face old foes Manchester United.
