Lukas Podolski nodded the Gunners in front after 11 minutes on Tuesday night, only for Shaun Maloney to give the visitors hope when he crashed home a free-kick on the stroke of half-time.
However, three goals in the space of eight minutes just after the hour from Theo Walcott, Podolski and Aaron Ramsey meant there was to be no fairytale ending for Roberto Martinez's men, despite another brave attempt at the great escape.
Arsenal will head to Newcastle in the knowledge victory on the final day of the Barclays Premier League season would secure another crack at taking on Europe's elite once again.
The Gunners are a point ahead of Tottenham, who host Sunderland, and two behind Chelsea, who have a better goal difference by just one.
Should Arsenal win 2-1 on Sunday and Chelsea draw 0-0 at home to Everton, then both London clubs would have identical records, with a one-off match at a neutral venue set to decide which side would go into the group stage rather than a qualifying tie.
Wenger, however, will focus on only securing victory to keep destiny in their own hands.
He said: "It is all open, but it depends on our result. Even third place is not out of sight if we win the game.
"In every single game until the end, for a long time now, we are in a position where we absolutely want the three points.
"I am confident because we have experience. We play for a long time under massive pressure and we have always found the solutions with the problems that we have faced."