The outgoing leader, who will remain in Parliament as MP for Maidenhead after leaving Downing Street, said she had achieved an "enormous amount" in three years in the job, but was sorry having to leave when "there was more that I wanted to do".
May and her husband Philip will depart Downing Street on July 24, after being succeeded as Prime Minister by either Boris Johnson or Jeremy Hunt.
She was forced to announce her exit in May, amid a revolt by Conservative MPs unhappy about her failure to take the UK out of the European Union (EU) on March 29 and her decision to open Brexit talks with the opposition Labour Party.
Interviewed in 10 Downing Street, May told the BBC she "didn't recognise" herself in criticisms that have been made of her personality and leadership.
But, despite having to go earlier than she wanted, May insisted she had been the "right person" for the job and was "immensely proud" of what she had accomplished.
Asked if she could have done more to persuade MPs to back her Brexit deal with the EU, which they rejected three times, she replied "One could always look back and say, 'If I'd sat down and talked to people more often'."
While wishing her successor well, she told the BBC she would continue to argue that leaving the EU "with a good deal" was vital.
And she called for a more discipline in government after years of leaks and political disagreements inside her cabinet "Good government depends on collective responsibility. It needs to return."
May assumed office on July 16, 2016, after then Prime Minister David Cameron resigned following following the outcome of the EU membership referendum in which 52 per cent of voters voted in favour of leaving the 28-member bloc.