Entwistle, who became the BBC's 15th director general on Monday (September 17), has called on the corporation to focus on creativity in its programming.
However, he was heavily criticised for his role in overseeing the BBC's television coverage of the Thames Pageant in June, as part of the celebrations marking the Queen's 60 years on the throne.
Stephen Fry branded the coverage as "mind-numbingly tedious", and the corporation was accused of dumbing down the reporting on the river parade, which featured hundreds of boats sailing past the monarch.
More than 1,000 complaints were submitted to the BBC about the parade, including objections to the dreary programming and "inane" commentary.
Entwistle admitted that the BBC's coverage of the spectacle was "disappointing".
Interviewed on the Today programme on Wednesday (September 19), he said: "I would be happy to add my apologies to those already articulated by BBC people, particularly about the factual mistakes we made."
He added: "One of the key things for the essence of the BBC is to get its facts straight. We were genuinely thrown out of our stride by the weather."
Elsewhere in the interview, Entwistle said that the corporation would focus on providing more opportunities for women presenters, including roles on "factual programmes".
The BBC under his predecessor, Mark Thompson, was hit by various accusations of ageism and sexism, including a landmark industry tribunal case won by former Countryfile presenter Miriam O'Reilly against the corporation last year.
Discussing the future plans, Entwistle told Today presenter John Humphreys: "The key is to find people who have the right things to say, have expertise and bring them in. I know the BBC has to be better in this regard."
However, the new BBC boss added that he did not believe the solution was "turfing out a whole load of blokes who might be doing their jobs brilliantly with a view to getting women in".