The Gunners could not take advantage of rivals Tottenham losing on Saturday and Manchester United being held to a draw at relegated Huddersfield.
Instead, they too could only draw 1-1 with Brighton, Pierre-Emerick Aubameyang’s contentious penalty ruled out by Glenn Murray’s second-half spot-kick.
That leaves them three points adrift of neighbours Spurs in fourth and, with an inferior goal difference, it is now highly unlikely Emery will achieve his aim of taking Arsenal back into the top four.
The Spaniard can still take Arsenal into the Champions League if they can win the Europa League and they head to Valencia on Thursday for the second leg of their semi-final.
A 3-1 first-leg win at home last week has put Arsenal in the driving seat to advance to the May 29 final in Baku and Emery admits he is now focused on continental success.
“We had the idea to continue taking chances for the opportunity against Burnley next week, but today we drew,” he said.
“We know they are very organised and strong defensively, so the key was scoring the second goal. We tried to do that and they gave us some minutes to come back, and again we tried for the second goal and made chances, but their defence did very well and their goalkeeper made some big saves.
“I think we worked and tried but didn’t get the result for taking chances next week. Now our way is to be strong in our focus for Thursday.
“I think we can speak now about the different situations and issues in the season, but it’s better to focus for Thursday against Valencia – and we are going to do the analysis also in the Premier league, because it’s our first target and we didn’t take this position like we wanted.”
Brighton headed to north London having seen their top-flight status secured, with Cardiff losing at home to Crystal Palace a day earlier.
“The nice thing was that we were all together as a team when we knew the final outcome, which was obviously a big relief for us,” Seagulls boss Chris Hughton said after revealing he had not watched most of the game in Wales.
“We have been on the back of two dogged performances away from home. Wolves away, which was a big point for us, and of course nearly getting a similar result at Tottenham.
“Defensively we have been more of how we know we can be. Probably the areas that we have been short is getting the goals we need and that was the case today.
“We had to defend really, really well but I thought we had some chances to go and win it.”
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