The governing International Automobile Federation announced last year that, with some teams struggling financially, it planned to introduce a cost cap for next season with an agreement scheduled for June 2014.
However Todt, speaking to reporters at the Bahrain Grand Prix, said leading teams had made clear they did not believe the initiative was viable.
"I understand that all the [six] teams that are part of the strategy group are against the cost cap now," he said.
"So clearly, if the commercial rights holder [Bernie Ecclestone], and if six teams…are against, I cannot impose. It's mathematics. In this case, no more cost cap."
Under the new governance of the sport, a strategy group that includes six leading teams – champions Red Bull, Ferrari, Mercedes, Williams, McLaren and Lotus – have six votes. Ecclestone's Formula One Management has six and so does the FIA.
"In a way I am disappointed because it may be more difficult to achieve the reduction which I feel is needed," said Todt, who was attending his first race of the year.
"But everyone says we are all in favor of reducing the cost, and through sporting regulations."