The visitors came close on several occasions in the first half thanks to their free-flowing attacking play, although such chances all but dried up after the break.
The same could be said for Arsenal, with only substitute Robin van Persie testing Marseille goalkeeper Steve Mandanda in the second period.
Arsenal winger Theo Walcott admitted to feeling some frustration after the Gunners failed to make the most of home advantage.
When asked if he was frustrated at not being able to qualify, Walcott told Sky Sports: “Of course. We had the home support, we need to be winning our home matches, but yet again we were solid at the back, we managed to keep a clean sheet, but our strikers didn’t manage to get it in the net this time.
Defender Thomas Vermaelen played his first full 90 minutes since returning from injury, and he said: “It was hard work today. They (Marseille) are a good side with good players on the pitch and we had to work hard for this point.
“In the second half we had moments where we dominated the play but didn’t score.”