Thomson also said that the corporation has a case to answer over the lack of older women in key news and current affairs presenting roles.
He also acknowledged that the landmark age discrimination employment tribunal case brought by former Countryfile presenter Miriam O'Reilly last year had been an "important wake-up" for the corporation.
The BBC has been under fire over its perceived ageist and sexist handling of senior female presenters, including 54-year-old O'Reilly, who was dropped for more youthful presenters when Countryfile moved to primetime on BBC One.
There has also been criticism of the BBC's stance on newsreader Moira Stuart and ex-Strictly Come Dancing judge Arlene Phillips.
Acknowledging two key failures at the BBC, Thompson wrote in an article in The Daily Mail: "First, that there is an underlying problem, that - whatever the individual success stories - there are manifestly too few older women broadcasting on the BBC, especially in iconic roles and on iconic topical programmes.
"Second, that as the national broadcaster and one which is paid for by the public, the BBC is in a different class from everyone else, and that the public have every right to expect it to deliver to a higher standard of fairness and open-mindedness in its treatment both of its broadcasters and its audiences."
Thompson accepted that there are too few women among the BBC's senior on-air team, particularly in the big political interviews. He further noted that the strong proportion of women in senior executive and leadership roles at the BBC had not been reflected on screen.
"There has been a revolution at the BBC in recent years in the role women play in leadership positions. Of the 12 members of our Executive Board, five are female, all of them (and no, there isn't a completely satisfactory way of saying this) 'older' women," he wrote.
"Critical BBC services - including both Radio 4 and BBC Two - are in the hands of exceptional women controllers. BBC News, once an almost entirely male management domain, is largely led by women.
"But we've yet to see the same rate or scale of change on the air. In terms of interviewees on current affairs programmes like Question Time or Newsnight, it is a simple fact of life that many aspects of British national life are dominated by men.
"I believe these programmes do their best to find opportunities for women to appear, but David Dimbleby is right when he says that it would be wrong for the BBC to distort the reality of the distribution of power and influence in this country in the name of artificial gender balance."
Thompson, who is expected to step down after the London Olympics, pointed to a recent survey titled Serving All Ages which found that proportion of people feel that older women were invisible on television. The survey also indicated that more than a third of women over 55 felt that their contemporaries were not shown on screen by the BBC.
"That perception, and the reality behind it, is what we have to change," Thompson wrote.
He said that economics editor Stephanie Flanders was an example of the "outstanding" female talent on the BBC's political news team, but admitted that there are too few like her among the most senior on-air specialist journalists.