The Seagulls travelled to the French side needing a result after their opening Europa League 3-2 defeat to AEK Athens.
Matters were made even worse on Thursday night when Chancel Mbemba put the hosts ahead with an easy finish inside the area.
And just a minute later Lewis Dunk, who was named in the England squad earlier on Thursday, lost sight of the ball and allowed Amine Harit to run towards the penalty box before crossing into Jordan Veretout for the second.
The Seagulls thought they had a penalty as they appealed the ball striking the arm of a Marseille player in the box.
Referee Mykola Balakin appeared to be pointing towards the spot but it was revealed it was a free-kick to the Ligue 1 outfit for a foul by Jan Paul van Hecke.
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Brighton were then denied by a super save from Pau Lopez as both sides approached the break.
However, Pascal Gross netted in the opening moments of second half to give the Seagulls hope of a comeback.
Joao Pedro then secured a vital point late on as he netted a penalty after Tariq Lamptey was fouled inside the area.
Roberto De Zerbi's side have now conceded eight goals in two games across all competitions after their 6-1 defeat against Aston Villa.
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They are also winless in three matches across all competitions, with Chelsea knocking them out of the Carabao Cup last week.
However, Brighton have claimed their first ever point in European football as they eye the Europa League knockout stages.