Speaking at Stonewall's Workplace conference in London, the Labour MP criticised parliament, saying it "should look like the country we stand for and represent".
"The truth is, we don't have enough openly gay and lesbian MPs being selected for parliament, just as we don't have enough black and minority ethnic MPs and we don't have enough women MPs," Cooper said.
"We know that we have a huge amount more to do, both in Labour and across the other political parties," she added.
Also speaking at the event was broadcaster and economist Evan Davis, who suggested employers should learn from those in Silicon Valley who embrace difference and don't see diversity as simply a question of sexual orientation, disability or ethnicity.
"It's broader – you want to involve introverts and extroverts, optimists and pessimists, thinkers and people who do things," he said.
"Diversity doesn't just mean having people who fit a pre-assigned category but are otherwise identical to everyone else," he added.
Stonewall deputy chief executive Laura Doughty said: "People perform better when they can be themselves, and it's no coincidence that employers who recognise this perform far better than those who don't.
"It's fantastic to see so many great employers taking equality so seriously, and treating it as a significant factor in their success."
The conference gave over 600 delegates from major UK employers a chance to hear from speakers including broadcaster Alice Arnold, Paralympics GB women's sitting volleyball captain Claire Harvey, and Barclaycard CEO Valerie Soranno Keating.
ITV, Ben & Jerry's, Procter and Gamble and the Royal Navy were among the organisations sharing best practice with other employers.
