The Frenchman is in danger of missing out on Champions League qualification for the first time since 1997 which would deny the club a lucrative revenue stream.
But the manager said: "Financially we can live with not qualifying. On the sporting front? No. And the sporting front is the priority."
Defeats to Blackburn and Bayern Munich in the space of four days left the Gunners out of the FA Cup and on the brink in Europe but, according to Wenger, there is still a top-two finish to strive for.
He said: "We want to come back in a strong position in the Premier League. I feel apart from Manchester United, it is very open for all the other positions.
"So it is down to us to continue to be consistent like we have been in the Premier League."