Lord Tony Hall has said the BBC’s spending is "unsustainable" and admitted "we need to find more money".
The director-general also said there is a "threat" to the BBC and that the "cracks are beginning to show".
He has called on the public to support the BBC more and wants a debate on how it should be funded.
Speaking during the Royal Television Society conference, the BBC boss said that the broadcaster would not be able to compete and keep up with the rate of change due to licence fee cuts.
He urged people to support the public service broadcaster in an age of fake news and decreasing British content, as Amazon and Netflix continue to expand their share of the UK audience.
Lord Hall said: "While it looks likely other companies are taking over nationally, the BBC has had its funding cut.
"We need to find more money. The public doesn’t like cuts to the BBC. It’s their BBC and they want more from it, not less.
"We do not believe what we currently do is sustainable with the pressures we face. The cracks are beginning to show.
"We have lost BBC 3 as a network presence, we have lost our Formula 1 coverage.
"There have been cuts to the licence fee. Our competitors do not face the challenges we face."
The BBC boss made the plea for support while highlighting the importance of the BBC in battling fake news and disinformation, adding "our democracies are being undermined".
He stressed the need for a trusted public service broadcaster, but said the BBC required more funding just to maintain its current programming.
Lord Hall said that despite reducing company running costs to just 6% after numerous efficiency savings, the BBC would still need to spend more "just to stand still".
He did not frame the plans as a cost-saving measure, but Lord Hall added more BBC staff and resources would be moved out of London in the future.