The 1 – 0 defeat to Aston Villa on Tuesday night leaves the Gunners in tenth ahead of the final day and they cannot finish any higher than eighth.
Arsenal haven’t finished below sixth since 1995.
For the fourth year in a row, north London rivals Tottenham will end the campaign above them.
Granit Xhaka said Arsenal were not good enough in their 1-0 defeat to Aston Villa on Tuesday.
“I think it was Aston Villa, their fight, they put everything out in each half and in my opinion they deserved the three points.
“We have a gameplan and we know they are very strong on set pieces but we did too many fouls near our box, too many corners against them but we didn’t play our gameplan. They were more aggressive than us and deserved it.”
The result was disappointing especially considering they had beaten Liverpool and Man City in their last two games.
Xhaka added: “Yes, of course, to beat two big, big teams… but in my opinion you can’t come here and play like this. It’s not good enough and you can’t play with this mentality.
“It was not enough to take something from today, and we knew if we won today, the last game if we won as well we could have got into the Europa League, but now we have to win the FA Cup and we have more pressure. But we will do everything to win the FA Cup now.”