Facebook’s Sheryl Sandberg has called for public policy changes to help improve women’s pay and claimed that women underestimate their worth, which prevents them from asking for wage rises.

Sandberg, the chief operating officer of Facebook, told BBC Radio 4’s Desert Island Discs on Sunday she believed job openings should be contested by equal numbers of women and men.

“We need to start paying women well and we need the public and the corporate policy to get there,” she said. “Certainly, women applying for jobs at the same rate as men, women running for office at the same rate as men, that has got to be part of the answer.”

Her comments come after the row over gender imbalances at the BBC following the publication of pay rates for broadcast talent, which revealed wide gaps between the earnings of male and female colleagues in some departments.

Sandberg is estimated by Forbes magazine to be worth $1.7bn (£1.3bn), but she told the Desert Island Discs presenter Kirsty Young she experienced self-doubt while studying at Harvard and recognised that women underestimated their worth more than men, which stopped them putting themselves forward or asking for a pay rise.

Her position appeared to echo that of Sir Philip Hampton, the non-executive chairman of drugs company GlaxoSmithKline, who has been tasked by the government with working to remove barriers preventing women from rising to senior business posts. He came under fire last week after saying he had “never, ever had a woman ask for a pay rise”.

Sandberg, who chose Beyoncé’s Run The World (Girls) as her first song, said: “We start telling little girls not to lead at a really young age and we start to tell boys [to] lead at a very young age. That is a mistake. I believe everyone has inside them the ability to lead and we should let people choose that, not based on their gender, but on who they are and who they want to be.”

She also talked about her grief following the death of her husband Dave Goldberg in 2015. “I didn’t know anyone could cry this much,” Sandberg said.

She chose One by U2 as the record she would keep if the other seven were washed away, because Goldberg had loved the band. Sandberg also chose Queen’s You’re My Best Friend in tribute to her group of close female friends, who she said had supported her through the ordeal.