Kieran Richardson opened the scoring at the Stadium of Light, before Alex Oxlade-Chamberlain was unfortunate to get the final touch to score an own goal for the second.
The Gunners now need to overturn a four-goal deficit against AC Milan in the second leg at the Emirates to stay in the Champions League.
The north London club were last crowned with a major honour in 2005 when they won the FA Cup in a penalty shootout against Manchester United.
With the wait for silverware set to continue at the Emirates and pressure mounting on the Frenchman, Goal.com wants to know if you think he should now part ways with Arsenal.
Jonny M`tui on Twitter: "the same mistakes wenger is ever making.cal it a quit."
Michael Fisayo on Twitter: “wenger isn't interested in trophies just wanna make more money for the investors, that's they are still keeping him till date.”
Peter White on Twitter: “This can't continue,i hate blaming managers but if they don't win this for Wenger then the end is nigh #no backbone.”
HAVE YOUR SAYDo you think Arsene Wenger should leave Arsenal now? Or do you think the players are to blame? Maybe the club should wait until the end of the season? Let us know your views by voting in our poll and by leaving a comment below. You can also interact with us and other readers on the Goal.com Facebook and Twitter pages. The top comments and the poll results will be published in the near future.