"Somebody can have 10 billion in the bank but it doesn't mean they are going to spend it," Ecclestone was quoted by F1 business journalist Caroline Reid.
Haas confirmed on Monday that Haas Racing Development has already paid the $5000 application fee to the FIA, after the governing body invited interest in the vacant 2015 team slot.
But "Mr Ecclestone doesn't think I have enough money to do this," Haas is quoted by the Associated Press, admitting the 83-year-old Briton was being "brutally honest" when he issued the warning.
"He doesn't think we will get the license. So my chances probably aren't that great of a shot," he added, revealing that he has also had a few meetings with Ecclestone.
Vowing to double the profits of his machine manufacturer Haas Automation to $2 billion a year, however, many believe that if any racing enthusiast has the money for F1, it is the Californian.
So why Ecclestone's pessimism?
"That's a little bit of a letdown," Haas admitted, according to USA Today.
"I respect the man, and it's a very difficult sport, the highest echelon of racing in the world. They want teams that compete and stay for 10 years.
"If Mr Ecclestone is saying we don't have a chance of getting a license, it would be foolish to continue. I'm not sure what he's trying to tell us. Maybe that it's a very difficult sport.
"We've submitted information. Maybe we don't have what they want.
"I don't think it's black and white," he continued. "It's their process. You have to be respectful of that. If you push it, seems it doesn't work at all."
It could be that Ecclestone's comments are the result of Haas vowing to go his own way, despite the fact existing competitive teams require mammoth annual budgets.
"The big teams spend $200 to $300 million but have 10 engineers working on one fitting," said Haas. "I don't think we'd approach it that way. But I can be naive, too.
"I just think we as Americans have the ability to take complex machines and figure out how to make them go fast without all the complexity. I could be wrong, but I have that gut feeling," he explained.
"Everybody said I'm out of my mind," Haas continued, "but the shock was when Mr Ecclestone said I don't think these guys know what they're doing. That's tough to overcome.
"I won't know until I try," he is quoted by the Charlotte Observer. "If you don't try, you'll never fail."