There's been speculation De Zerbi could be dumped by Marseille after their elimination from the Champions League this week.
There even claims De Zerbi could be removed before the weekend clash with Paris FC.
However, the Italian said on Friday: "We lost an important match. We're out of the Champions League. We need to try and understand.
"(President) Pablo Longoria and (sporting director) Medhi Benatia, we spoke last night. We met to try and find the best possible solution.
"This match is also partly my fault. We'll do everything to bounce back. I'm still here."
Asked about reports he was considering offering his resignation, De Zerbi also stated: "I really wanted to come to Marseille. That's the truth. There's also the element of responsibility. I was taught to take responsibility. I'm telling you, the club, we played a bad match, that's all.
"I don't know if I'm the ideal coach for OM. From a results standpoint, we've done some good things. But there's this lack of consistency."
De Zerbi added, "I have the strength to stay in Marseille for another 5 or 6 years because I have the passion, I love it.
"The players support me. What annoys me is defeat. It's not a question of passion but of powerlessness. These are defeats that leave their mark, but the players have great human and sporting qualities."