Steiner thinks it would have been 'almost impossible' for Haas to have stayed in F1 unless there had been a shake-up of F1's finances.
Following months of uncertainty about the future of the American-owned outfit, with Haas admitting he was unsure about whether or not he would remain in F1, the team last week announced that it had signed up to the new Concorde Agreement.
That effectively means Haas is committed to stay in grand prix racing for the next five years.
Steiner is convinced, however, that without the radical cost cuts being planned for F1, including a budget cap, allied to a more equal share of the sport's prize money for all teams, the outcome could have been very different.
Asked by Motorsport.com if he felt he could have convinced Haas to stay without the changes to the sport's finances, Steiner said: "I would say it would have been a lot more difficult and almost impossible if there wouldn't have been the chance to be competitive, and also that the spend would not increasingly go up.
"For sure, having more income helps always because the gap between what you can spend and what you get is smaller. So, I think without these two changes, it would have been very, very difficult that Haas would be around for the future."
Ultimately, Steiner thinks the key factor speaking in F1's favour was the huge marketing exposure the sport gives Haas' business.
"I think the main thing is he sat back and saw F1 is, marketing wise globally as a tool, very powerful. And for him thinking about what it did over the last five years, for sure it was beneficial to his company, for Haas Automation. That was the main reason.
"And then, for sure, all the other things like the Concorde Agreement and more equal payouts and the budget cup, that worked as well to convince him that this is a place to stay.
"I think without the alignment or the semi alignment of the payouts to the smaller teams and the big ones, and the cost cap, without that one, I'm really convinced he wouldn't have signed up for it because it's just so difficult to catch up."
While Haas was open that he was weighing up whether or not to stay in F1, Steiner said he was never worried that his boss would decide to pull out.
"Worried is a big word," he said. "I was more focusing to give him solutions for what he was looking for, and negotiate solutions, so that somebody like Mr Haas is convinced F1 is still a good investment. That's what I was doing.
"I wasn't worrying. I was working hard because if you start to worry you make emotional decisions, and they are normally wrong. So it was keeping in touch with him, explaining how we should be doing it, and talking with him and talking it through and getting his input.
"He has got some good ideas, so it was just trying to find ways to get them within the Concorde Agreement, and we did that with the financial agreements. So that's what we did.
"Therefore I was never worried. It was more like how can we make this work, because if it doesn't work, then he wouldn't do it? If it doesn't work for him as a marketing tool, why would he do it? That was my job.
"So the worry was actually not big, I was just working hard and trying to do my best that he continues."