Emery has come under fire from sections of the Arsenal support following a lacklustre spell, and a meek second-half display on Saturday evening saw their anger intensify.
Sky Bet reacted by making Emery 15/8 in their revised sack race market - putting the Spaniard at the top of the market alongside Southampton boss Ralph Hasenhuttl.
"For me, as a coach, it's about continuing stronger and improving with our players," said Emery.
"I am speaking with the club to stay calm and to stay patient to improve and recover some confidence with some circumstances.
"We are receiving criticism but I know that's my job. I've had lots of moments like that but I've recovered by working to get confidence, being together with the club and players.
"I accept all (of the criticism). I accept the applause and I accept it when they criticise us. I know when we win, they are going to be happy and when we lose, they are going to be sad. It's normal.
"We need to stay calm and also keep improving things. Today we got one step ahead by being together and being strong defensively. But we lost because we were playing a very strong team in a good moment."
Arsenal had chances in the first half at Leicester, but after the break their attacking threat became virtually non-existent and, from the moment Jamie Vardy put the Foxes ahead, the result was effectively beyond doubt.
In fact the Gunners failed to produce a single shot from the 53rd minute onwards, but Emery maintains they had a game plan which was largely executed.
"We can be disappointed with the result but with the attitude of the players, they did the game plan we prepared for.
"We started the first half by having chances by controlling the game, and at the start of the second half too, in our moment like we wanted.
"The attitude was good, the game plan was prepared for and the players did that. The other team are in a good moment, at home and feeling strong."
Leicester, now odds-on for a top-four finish, head into the international break on a four-game winning run in the Premier League and with a nine-point gap back to Arsenal.
And they have a chance to further underline that their aspirations may be greater still, with a sequence of kind-looking fixtures before they face Manchester City and Liverpool either side of Christmas.
