Jamie Vardy and James Maddison were the architects of another fine victory for the Foxes, who moved into second, as the English duo struck in the space of seven second-half minutes.
A return to the Champions League next season was Emery’s target after a summer of heavy investment in reshaping his squad.
But Arsenal will fall nine points behind the top four should Manchester City avoid defeat away to league leaders Liverpool on Sunday.
“We are very ambitious in our target, but we know we need time and patience,” said Emery, who faces an anxious wait to see if his wish will be granted by the Arsenal board with a two-week international break coming up.
After early signs of promise at the start of the Spaniard’s reign last season, Arsenal have now taken fewer points in Emery’s first 50 Premier League games in charge than the final 50 of Arsene Wenger’s 22-year tenure.
In the face of mounting speculation over his future, Emery surprisingly maintained Mesut Ozil alongside the front two of new captain Pierre-Emerick Aubameyang and Alexandre Lacazette.
That bold strategy nearly paid off when Lacazette fired the first big chance of the match inches wide after Aubameyang had burrowed his way into the area.
“If we score the first goal, we could have controlled the game. We didn’t do it and they did,” added Emery.
Thereafter, it was Leicester who showed the greater threat going forward.
Wilfred Ndidi missed a glorious opportunity when he smashed off the crossbar with the goal gaping from Ricardo Pereira’s cutback four minutes into the second half.
Arsenal were the first to put the ball in the net when Aubameyang supplied a characteristically clinical finish but was rightly flagged offside.
Vardy has an excellent record against Arsenal and when his chance came, the Premier League’s top scorer was ruthless with a low finish past Bernd Leno from Youri Tielemans’s pass.
“It was a brilliant goal and from there I thought we took control of the game,” said Leicester manager Brendan Rodgers.
Vardy turned provider for Leicester’s second as he laid the ball back into the path of Maddison to drill a low shot in from outside the box.
“People say they enjoy watching us but we enjoy playing so much. It’s a great feeling,” said Maddison.
Arsenal offered precious little after going behind and have now won just two of their last 10 league games.
