The FIA announced a budget cap will be introduced from the start of 2015 following a meeting of the F1 Strategy Group and the F1 Commission in Paris on Monday.
The need to take action and cut costs has become increasingly urgent in recent years, with the majority of teams struggling financially.
Speaking before the announcement of a 2015 budget cap however, Whitmarsh warned that F1 teams' collective self-interest would always threaten to undermine or even derail attempts to restrict costs.
"If we want to do it [introduce a budget cap] we have got a way of doing it, but a minority will always be opportunistic or try to frustrate it," Whitmarsh told AUTOSPORT.
"There have always been and will always be 'haves' and 'have nots', [and] the problem is that the 'haves' never want to deal with it.
"It is so easy to have unforeseen consequences and changes in a finely balanced situation.
"I think it can be done, but if there is not a big enough will..."
Whitmarsh admitted there was cause to implement a budget cap, but said his own efforts at mediating spending had proved dispiritingly futile.
He also pointed to the shortcoming of the Resource Restriction Agreement as evidence of just how difficult a budget cap will be to enforce.
"The RRA achieved certain things and it could have achieved a lot more," Whitmarsh said.
"It was a proper professional process. This idea that we are going to sit in a room for half an hour and solve all the problems is not realistic.
"There isn't a silver bullet.
"Ultimately teams cannot carry on spending more than they get coming in.
"To be frank I spent too much time trying to be the good citizen in the sport, and no one is ever going to thank you for it. I probably ought to concentrate on other things these days.
"The sport works better in crisis; that is just the way it is I am afraid."