Experienced goal-poacher Inzaghi, carelessly left unmarked at the far post, put the visitors ahead on 28 minutes when he tapped in from close range after a perfect cross by playmaker Clarence Seedorf.
Marseille recovered to level four minutes into the second half, Argentina defender Gabriel Heinze heading home from a Benoit Cheyrou free kick.
"This was a good show from us, especially in the first half, and this is a good result but it's too early to say we're back," Tassotti said. "What we need is a string of good results."
"Tonight we saw the difference between a good French team and a great European side," Marseille defender Souleymane Diawara told reporters.
"We were inattentive twice and they scored two goals. We will learn from this for our next matches," he added, looking forward to matches against Real Madrid and FC Zurich.
Looking more and more confident, Marseille went on to create a few more chances but the Milan defence held tight and then Inzaghi lived up to his reputation as one Europe's most-feared marksmen.
The match was tense and marred by a few ugly scenes, notably a dangerous tackle from Milan's French midfielder Mathieu Flamini. The former Marseille player was lucky to escape with just a yellow card for his second-half challenge on Stephane Mbia.
