The Gunners missed the opportunity to rise to third after going down to a 1-0 defeat thanks to Phil Jagielka’s early strike.
It means Arsenal could drop out of the top four on Monday as rivals Chelsea, who are level on points with the Gunners, face West Ham at Stamford Bridge.
The game was a frustrating one for Arsenal and playmaker Mesut Ozil even threw his jacket in the direction of Toffees boss Marco Silva shortly after being substituted.
However, Arsenal’s destiny is still in their own hands and while Emery was frustrated at his players failing to execute the game plan, he was quick to point out that they are in a good position to challenge for the coveted Champions League spots.
Emery refused to do radio interviews after the match but addressed the print media in a press conference.
He said: “We knew it was going to be very difficult today but we are going to have chances in the next matches and it is still in our hands to take the chances to be in the top four.
“I don’t think we are very bad. It is a bad result and not a good performance but we are fourth.