The Gunners will play the Turkish side in Istanbul on Tuesday evening, before hosting the second leg days after a trip to Everton, and the Frenchman is aware of the importance of all three games.
He told reporters: "It is a big test. We have had a short preparation and we know that in one week we have three big games with Besiktas home and away and Everton in between.
"We have to be on our toes. We were not completely happy with our performance last Saturday (against Crystal Palace) and we want to improve.
"I have good experience of the Champions League. I know you have to be pragmatic, but first we have to qualify. Before we can speak about anything else we have to put in two big performances against Besiktas."
The trip to Besiktas is the second successive year that the Gunners have played a Turkish side for a place in the Champions League, following last year's victory over Fenerbahce.