"With proven funds and sporting success that has earned us a place in European competition for two consecutive years, we sincerely do not understand how an administrative decision could relegate such a major French club," Lyon's statement said.
"We will appeal to demonstrate our ability to provide the necessary financial resources to guarantee OL's place in Ligue 1."
Seven-time French champions Lyon raised around £45m with the sales of Maxence Caqueret to Como in January and Rayan Cherki to Manchester City in June in an attempt to improve their finances.
High earners such as Alexandre Lacazette and Anthony Lopes have also been released.
Lyon have the right to appeal against the decision. Should it stand, Lyon will be replaced in the top flight by Reims, who were beaten in the relegation play-off by Metz.
Only five teams have lifted more French titles than Lyon's seven, which they won in successive seasons between 2002 and 2008.
The club reached the Champions League semi-finals as recently as 2020 and have not played in the second tier since 1989.
When the provisional punishment was handed down in November, Textor said that there was "no chance" the club would be relegated and reiterated his confidence before Tuesday's meeting.
"We have made a variety of investments in recent weeks," he said. "Everything is good financially."
Textor is also the largest shareholder of Brazilian club Botafogo and currently co-owner of Palace until his deal to sell his stake to New York Jets owner Woody Johnson is completed.
"Over the past few months, we have worked closely with the DNCG, fulfilling all of its requests with equity investments that exceeded the required amounts," Lyon's statement continued.
"Thanks to capital injections from our shareholders and the sale of Crystal Palace, our cash flow has significantly improved and we now have more than sufficient financial resources for the 2025-26 season."
Palace qualified for the Europa League by winning the FA Cup but Lyon also qualified by finishing sixth in Ligue 1. The French side's higher league finish means they would take a European spot at Palace's expense - should Uefa decide their multi-club ownership rules are being breached.
Last year, six-time Ligue 1 champions Bordeaux had to surrender their professional status after being relegated from Ligue 2 to the French fourth tier because of bankruptcy.