The newspaper said the governor's office had confirmed that state payments to support the 2015 race would drop by more than 20 percent.
It said that this year's payment, based on a different formula for calculating how much economic activity the race generates for Texas, would be closer to $19.5 million than the previous $25 million.
"To use a technical term, I think we're screwed," said Circuit of the Americas chairman Bobby Epstein, who has to pay Ecclestone a significant annual sum in race hosting fees.
"The state clearly made promises. I think we made a deal, and we lived up to our end of the deal," he said of the recalculation.
"It's like if you go to a restaurant and order a dinner, and then after you've eaten the meal they change the price."
The Austin circuit is Formula One's first purpose-built track in the United States and has hosted a grand prix since 2012.
This year's event, which saw Britain's Lewis Hamilton take a third world championship last month, was badly hit by the weather with Epstein saying the heavy rain had been "financially devastating".
Saturday's final practise took place behind closed doors and, when fans were admitted, qualifying could not go ahead and was postponed until the Sunday morning.
The race also attributed the reduced crowd in part to the return of neighbouring Mexico to the calendar after a 23-year absence.
The race day crowd in Mexico City was put at 135,000.
"The big question now is: "Is the race coming back?," Epstein told the newspaper.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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