The Russian had his F1 contract with Haas terminated earlier this week in the wake of the fallout of his country's invasion of Ukraine.
While Mazepin feels Haas's actions were unfair, as he says he was ready to compete under a neutral status as the FIA had allowed, he has vowed to do all he can to help those who face similar difficulties to him.
Speaking from Moscow in a video conference with media on Wednesday, Mazepin said that his 'We compete as one' foundation would be funded by money from sponsor Uralkali that had originally been intended for Haas.
Uralkali is currently seeking legal action over Haas to repay any sponsorship money for 2022 that had already been received by the team.
Mazepin explained that the foundation would help provide support, both financial and non-financial, to athletes who could not compete. This can include legal aid to fight cases, as well as mental health aid.
"The decision from Haas was not based either on any directive from the sport's governing body authority, or dictated by any sanctions that were placed against either me or my father, or his company," he said.
"And, of course, I don't feel this is fair.
"But there is something more important here. I ask the question, is there no place at all for neutrality in sports?
"Does an athlete have a right not to just an opinion, but to keep the opinion out of the public space? Should an athlete be punished for that? And do we want the sports to become just another public square for protests and political debate?
"We all know cases where one country refuses to compete with another in the Olympics because of their political disagreements. We saw in the 1980s that a generation of athletes lost their dreams and the chance to compete at the highest level when countries started boycotting one another.
"Is this where we want the sports to be? Or are sports a way to bring people together, even at the toughest times, and especially at the toughest times. My experience in the last few days has greatly informed my thinking on these questions."
He added: "We all know that the career of an athlete is a short one, and that it requires years of intense sacrifice to perform at the highest level. When that final reward is taken away, it is devastating. And no one is thinking what happens next to these athletes. I will be addressing this."
Mazepin has not given up totally on a potential return to F1 in the future, but says for now his focus will be on the foundation rather than getting back behind the wheel.
"I absolutely do not see F1 as a closed chapter for me," he said. "I am going to stay in a race condition. And I will be ready to take on an opportunity if it comes. And at the moment, I'm only sighting F1 and no other categories.
"I do not plan to participate in different series and different championships. I will now focus all of my attention and time to work with this foundation that I have established."
He also revealed that he had received messages of support from a number of drivers regarding the situation he found himself in.
"I actually highly appreciated the small number of drivers who expressed this to me, for instance, Sergio [Perez], Valtteri [Bottas], Charles [Leclerc] and George [Russell], they all contacted me.
"I would also like to add that I'm thankful for the support from them, because in the long journey towards F1, they've been, every one of them, risking losing their seats, and they actually support me in this time when I lost my dream, and I lost my drive."
Mazepin did not wish to get too drawn in to commenting on the war in Ukraine, but admitted that it was a "painful" time for everybody.
"I want to say, first of all, that I understand that the world is not what it was two weeks ago," he said. "And I get it. For me, along with all of you here, I'm sure that this has been an extremely painful time.
"Those who do not live in this part of the world, or were not born here, will see only a part of it. Those of us in Russia or Ukraine, see it on many more levels.
"As all of us, I have friends and relatives who have, by force of fate, found themselves on the both sides of this conflict. What we're discussing today is important in its own way, but nothing in comparison to what is going on in the larger picture."
