However, despite failing to ensure progress on the night with a victory, Arsenal are still well placed to advance as they top the standings with eight points from four games, with Marseille second on seven.
Borussia Dortmund have four and Olympiakos three after Dortmund, who visit Arsenal in their next match, won the group's other game 1-0.
Tuesday's match was something of a repeat of the team's Velodrome meeting last month - without the late drama when a stoppage time goal from Aaron Ramsey gave Arsenal a 1-0 victory.
The Londoners, recovering from a slow start to the season with five successive wins, were lacklustre on a night manager Arsene Wenger opted to start without Robin van Persie, the hat-trick hero of Saturday's 5-3 win at Chelsea.
Wenger said he decided to rest the Dutch striker, adding that he thought the emotional strain of Saturday's win at Chelsea in the Premier League had an effect on his team's performance.
Van Persie came on for the later stages but even he failed to find the spark that would have ignited the home side's performance, although he did have one good chance when he attempted to chip goalkeeper Steve Mandanda who easily saved his effort.
Knowing a point would keep each side on course, neither were prepared to risk too much, with the result that neither took control of the game and neither created many chances as Arsenal stretched their unbeaten run in home group stage matches to 25 games dating back to 2003.
Wenger told reporters afterwards: "We wanted to qualify tonight, but we were not at our sharpest.
"Marseille started stronger than us, but after we got back in the game we had some opportunities to kill it.
"But you have to give credit to Marseille - they defended very well and we were not sharp enough. We were emotionally tired after Saturday's win but we remain on target and know we can do better."
Marseille manager Didier Deschamps, back in London where he spent a season with Chelsea, was relatively happy with the outcome which keeps his team's chances alive too.
"I feel we dominated them at times and we put them under some pressure. I am quite happy with a point away from home, and we still have the chance to qualify."
DEFENSIVE AUTHORITY
Marseille, starting brightly with an effective 4-4-2 formation with either Andre Ayew or his brother Jordan joining Loic Remy up front, could have taken the lead after six minutes when Andre stabbed the ball just wide of Wojciech Szczesny's left-hand post after a good move involving Remy in the build-up.
Theo Walcott had Arsenal's first chance after 10 minutes when he hit a low drive just wide, but with Souleymane Diawara doing an effective job in the front of his back four, Marseille limited Arsenal's attacking options with some degree of defensive authority.
Aaron Ramsey, scorer of Arsenal's last-gasp winner in the first match two weeks ago, had two good chances but failed to convert either of t
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