Speaking to Victoria Derbyshire on BBC Radio 5 Live, Bennett also admitted that the ongoing controversy over the BBC's senior executive pay is "damaging the BBC".
Bennett said that the corporation is looking to reduce costs "across the board", meaning "fewer flights and more trains and so on".
The director claimed that on-screen talent faced "double digit decreases in their fee structure on television", while the corporation would continue to "drive quite a hard bargain".
She said that she had "no hard feelings" towards Adrian Chiles, who quit The One Show to join ITV after objecting to Chris Evans being drafted in to present the programme on Fridays.
"I hoped that Adrian would have looked at the different types of projects we had put on the table, I have always been a big fan," she said.
"Talent in this industry does move around, it was a case of it being weighed up in different ways. Football was a big attraction from ITV which they put on the table.
"The Friday question was a big decision, I accept that. We are rethinking Friday as a whole, not just The One Show. We wanted to bring in different types of elements of entertainment on a Friday and Chris Evans was someone I really wanted to have as part of the channel."
Bennett defended the BBC's decision to withdraw a contract offer to former The One Show presenter Christine Bleakley, who subsequently joined Chiles at ITV.
"How long to wait for a decision to be made [over a contract] is part of my job. At some point negotiations have to come to an end," Bennett said.
"We had been open to continuing discussions up to a point, to leave it too long would have meant not knowing what we were going to be doing. I did it regretfully, I don't normally have to do that, in the end it dragged on and on."
Asked out Chiles and Bleakley's new breakfast programme Daybreak, Bennett said: "I think that I quite like the look over London [from the studio].
"That kind of programme will have to bed down, there are a lot of elements in it, obviously a big change. Programmes have to be given time. I wish it well."
Bennett also defended the corporation's legal battle to prevent racing driver Ben Collins from revealing his true identity as Top Gear's The Stig, which she described as like "unmasking a superhero".
"The Stig is a great character. Imagine if you had Mickey Mouse or a superhero being unmasked every time, you start to have the magic of the show chipped away at," she said.
"The Stig is a character and creation of the Top Gear team, and a creation of the BBC and is in effect owned by the audience. The pleasure of the show is part of that magic not being destroyed. We think it is important to protect the audience's enjoyment and the magic of the show, and not unmasking our superhero character.
"There is also a contract involved... and intellectual property. These are creations through public money which other commercial concerns are exploiting. For us not to have regard to that wouldn't make us a professional broadcaster and media company."