Motorsport boss Max Mosley has warned that there is a "serious danger" another car manufacturer could follow Honda out of Formula One.
Mosley, president of governing body the International Automobile Federation (FIA), said Honda's exit was "very sad but it's not entirely a surprise".
Mosley said it was imperative the sport cut its soaring costs - with top teams spending about £300m a year.
Mosley derided the team's cost-cutting proposals as "fiddling about".
The Formula One Teams Association (Fota) met on Thursday to discuss its own proposals and said they had agreed to "substantial cost-cutting for 2009 and 2010, and additional initiatives to improve the show".
Fota also agreed a "new, low-cost engine will be introduced in 2011".
The organisation said it would submit these proposals to the FIA, but Mosley said on Friday that they did not go anywhere near far enough.
If we don't cut costs, we would lose one team after another and we would end up with no teams at all, or a grid that lacked all credibility
Max Mosley President, motorsport's governing body the FIA
He described Honda's decision to quit F1 and try to sell its team as a "very significant warning".
"If the teams don't notice now what's happened, you have to abandon all hope for them," he added.
"The teams who met are all subsidiaries of these big companies and they could get a fax in the morning saying: 'We're stopping this, which is effectively what happened with Honda.
"So if they don't wake up to it now, they'll probably get a nasty shock in the future.
"But our job is to take action to make sure that won't happen. That's why we've sent out a letter to the teams this morning setting out or plans to get the costs right down."
F1 commercial supremo Bernie Ecclestone played down Mosley's claims that the sport's future was at stake.
"F1 is in no bigger crisis than any other company in the world at the moment but the world won't stop, that's for sure," he said.
Mosley said no changes could be made to the rules for 2009, but that he would make dramatic changes for 2010.
He says the FIA can supply a standard engine and gearbox to teams through a central supplier for 5m Euro (£4.3m) a year, as well as a standardisation of some chassis parts.
Teams would be able to design their own version of that engine, or continue with their current designs restricted to ensure they had no advantage.
"The danger with these big companies is they may follow Honda, so if we make it possible for them to compete very inexpensively, by their standards, then the situation is much safer," he stated.
"The objective has to be to enable a team to say to manufacturer: 'We can actually get by without a subsidy.'
"If we can achieve that, then I think we will keep the manufacturers in.
"If we can't, then when they're looking to cut costs - which all of them are now because car sales have collapsed - then they will start to look at F1 and say do we really need this, and come to the same conclusion as Honda."
He said he would not be diverted from his plans.
I've no doubt Honda would have been in top four next year without any problems
"Our position is very simple. We will say, these are the rules for the 2010 championship.
"If you don't want to enter, you don't have to. If you'd like to set up your own series with unlimited expenditure you can do so, but if you want to run in the F1 world championship these are the rules."
He said that if nothing changed, F1 "would lose one team after another and we would end up with no teams at all, or a grid that lacked all credibility".
Ecclestone added: "[Honda's departure is] a shame because everyone's been working like crazy to reduce the necessity to spend to be competitive.
"Yesterday there was a meeting of the technical people in order for this to take place. I've no doubt there would have been a drastic reduction in cost and the necessity to spend to be competitive, which is what we've been trying to do.
"I've no doubt Honda would have been in top four next year without any problems.
"They've spent a lot of money to put themselves in that position so if anyone does want to be in F1 this is a team they should look to buy.
"It's a big opportunity for any company that's run efficiently to benefit."
McLaren chief executive officer Martin Whitmarsh, chairman of Fota's sporting commission, said: "It goes without saying that we hope a satisfactory resolution can be found [to the Honda team's plight].
"Clearly, in the current economic climate, F1 faces a significant commercial challenge. But, on a positive note, Thursday's Fota meeting in London was very constructive.
"So, acting together in the context of Fota, and in co-operation with the FIA and [commercial rights holder] FOM, the teams will continue to work hard to adapt the cost structure of the sport so that it can pull through the global economic downturn and remain in good health throughout these turbulent times."
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