Julia Gillard has expressed her disappointment for “friend’ Hillary Clinton. Picture: Ella Pellegrini

Australia’s first female prime minister appeared at the 10th annual Cosmopolitan Women of the Year Awards in Sydney yesterday after Donald Trump defeated Ms Clinton in the US presidential election.

“It is good to be here with all of you after what was I think a fairly gut-wrenching day and night for many of us as we watched the results come in from the US election ... It is something that I think is playing very heavily on us,” Ms Gillard said.

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Former Prime Minister Julia Gillard at the 10th annual Cosmopolitan Women of the Year Awards in Sydney. Picture: John FotiadisSource:News Corp Australia

She continued: “I think all of us did want to see that big glass ceiling shattered. We did want to see President Clinton and we did want to have that moment of celebration today. I am disappointed. I am disappointed personally for my friend Hillary.

“I am disappointed that women and girls around the world have yet to see that example, but I am also determined that we will see that example. So much has changed so positively for women and we’ve got these next weeks to fight for and I know we are going to do it together.”

Like Ms Clinton in her concession speech, Ms Gillard encouraged the audience of women not to be deterred by failure.

“It is this generation that will break down the final set of barriers for women in our society. It will be members of this generation who will rise in record numbers to go to the top of politics, business, the judiciary and civil society and don’t let yesterday’s disappointment dissuade you in any way,” she said.

Prime Minister Julia Gillard (left) and US Secretary of State Hillary Clinton attend the Equal Futures Partnership event at The Intercontinental Hotel in New York on September 24, 2012. Picture: SuppliedSource:Supplied

Ms Gillard understands Ms Clinton’s disappointment all too well. She became Australia’s first female prime minister in June 2010 but was replaced in a June 2013 leadership spill by Kevin Rudd, the man she ousted three years before.

Hours after Ms Clinton’s shock defeat, Ms Gillard tweeted her support for the Democratic candidate.

“Thanks @HillaryClinton for your courage. I’m still with her and her vision of inspiring girls by shattering that high, hard glass ceiling-JG,” Ms Gillard wrote.

Ms Clinton has made three public visits to Australia in the past 20 years, during which time she forged a close bond with Ms Gillard, spoke warmly of the warm relationship enjoyed by the two nations, and declared a surprise dislike for Vegemite.

In her book, Ms Clinton lashed out at the “outrageous sexism” endured by Ms Gillard as prime minister.

The pair met several times while Ms Gillard was in office. Ms Clinton praised Ms Gillard for her famous misogyny speech, noting how many women subjected to sexism would “just swallow it”.

“But she just went right at it and I respected that,” she told the ABC.

US Secretary of State Hillary Clinton (left) and Australian Prime Minister Julia Gillard walk along the Yarra River on the way to lunch at Melbourne's Federation Square on November 7, 2010. Picture: AFP/Pool/William WestSource:AFP

Former Australian prime ministers Paul Keating and John Howard have also weighed in on the US election result, revealing how they think Australia will fare under a Trump presidency.

Keating told ABC’s 7.30 Australia should move away from the US as a key alliance now that Mr Trump is at the helm, and instead look towards Asia.

“I’ve suggested for instance, we should join ASIAN, the Association of South East Asian Nations,” the former Labor leader said.

“In other words, we’d be more useful to the United States, by the way, if we were doing these things. Isn’t an independent, balanced foreign policy the right answer? Or do we stay in a crouch, saying Hail Marys to the alliance?”

But Mr Keating’s Liberal successor said Australia’s alliance with the US should endure.

“Those people who are talking about the need for some kind of radical recasting of our attitude towards the United States, forget the reality that this is a relationship so deeply embedded in history and sentiment, that it survives changes of personnel both in Canberra and Washington,” Mr Howard said.

Australians have mixed feelings about Mr Trump’s astonishing political ascension. Prior to polling day on November 8, an Essential Research poll showed Aussies weren’t especially optimistic about the prospect of Mr Trump moving into the White House.

Fewer than one in five thought he would be better for both the world and Australian economy, climate change, global security or Australia’s relationship with the US.

Hillary Clinton has lost her second bid for the White House. Picture: AFP/Jewel SamadSource:AFP