In a speech to the Voice of the Listener and Viewer conference, Thompson said that there was no getting away" from the need for "a significant reduction in services as well as job losses" at the BBC World Service division.
The global broadcasting unit is currently funded by the Foreign Office, but the BBC will take over financial responsibility from 2015 under its new licence fee settlement.
Under the deal, the TV licence fee will be frozen at the current level of £145.50 for six years to 2017 and the BBC will also take on funding for Welsh-language channel S4C and BBC Monitoring. The corporation will have to make savings of more than £500m to meet the new commitments, representing a 16% reduction in its income.
In his first speech since the settlement was agreed, Thompson defended the decision to reach a quick deal rather than "walk away from the table". He expressed his belief that the BBC would have been stuck with a much worse arrangement if it had tried to negotiate the settlement next year as initially planned.
However, Thompson also warned that there was a real danger that the BBC's independence could be "under-played or even forgotten" by the government.
Before the licence fee deal was agreed, ministers considered forcing the BBC to pick up the £556m cost of providing free TV licences for the over-75s, which both Thompson and the BBC Trust vigorously opposed.
"In my view, this move would also have called into question both the legitimacy of the licence fee for the remaining payers and the financial security of the BBC. It too would have damaged the BBC's independence," said Thompson.
"There was also the suggestion that the BBC should take on the responsibility for broadcasting some of the material commissioned and generated by the Central Office of Information, in other words government advertising.
"This too would be a fundamental and wholly unacceptable attack on the BBC and one we'd fight tooth and nail. The BBC is an independent public broadcaster, not a state broadcaster or an arm of government."
Thompson accepted that the corporation's decision to freeze the licence fee, along with its extra financial obligations, would lead to widespread cuts.
"Of course, it will be difficult to deliver," he said. "We believe that advances in productivity will not yield all of the saving and that the balance will have to come from what the technocrats call 'allocative efficiencies' and what most of the public rather reasonably think of as 'cuts'."
Former BBC chairman Michael Grade today claimed that the licence fee should be shared between the BBC, S4C and Channel 4 in a major shakeup of public service broadcasting.
However, Thompson said that he is confident the government will not place any further financial commitments on the £3.6bn licence fee in the near future.
He said: "This licence fee settlement should mark a high water mark of this whole approach. This is acknowledged in the agreement that sets out clearly that there will be no further calls on the licence fee, no new commitments."