The former France midfielder was unhappy with his side's profligate display against the Ligue 1 strugglers, and had bad news regarding the fitness of duo Andre Ayew and Loic Remy
L'OM disappointing result against Franck Dumas' men means they now languish 18 points behind Lille in Ligue 1's last remaining Champions League spot, and their coach openly accepts that his side have struggled to cope with the pressures of a demanding season.
"The situation is stressful for both the players and me, but we only have ourselves to blame," Deschamps told reporters after the game.
"We started a little labouriously, certainly due to our last game in the Coupe de la Ligue final, but in the first half we had enough opportunities to gain an advantage.
"The fatigue is there. We will not make excuses about it, but we played our 51st official match of the season.
"We have fought many intense battles with some players who have never experienced such a thing."
Reverting directly back to the draw itself, Deschamps then rued Marseille's missed chances but claimed he was encouraged by the endeavour his players showed throughout the encounter.
"Obviously this is a bad result for us, but we had trouble putting away our opportunities," he continued.
"This inefficiency does not suit us, but our intentions [to win] were there.
"We did a lot of good things in the match, but failed to take advantage of them. Nonetheless, we gave our all until the end.
The 43-year-old also revealed key duo Andre Ayew and Loic Remy may face spells on the sidelines through injury, a situation he admits is far from ideal.
"Yes, Andre has a shoulder problem, even though he played on Wednesday, and will soon undergo an operation," Deschamps added.
"Then there is Loic [Remy]. who has an ankle injury. This is not ideal because these two players are those who have been most effective for us."