Arsenal have qualified for the Champions League for 15 consecutive seasons - and Wenger says it is vital that run continues.
He said: "Financially we can live with not qualifying but on a sporting front, no.
"And the sporting front is the priority."
So finishing in the top four is arguably more important than winning a cup, according to Wenger.
He said: "The real quality of the team is judged on where you are on a consistent level in the championship and where you are in the Champions League.
"We are a bit short and we have to reduce that gap."