CANBERRA - Former Australian Prime Minister Julia Gillard broke silence for the first time since Kevin Rudd toppled her as leader of the Labor Party in June, revealing the grief, pain and regret over losing power and urging the party to rediscover its sense of purpose.

Gillard has written a 5,000-word essay on Labor's lessons and future for the Guardian Australia website, which ran the piece on Saturday.

In the article, Gillard said "losing power is felt physically, emotionally, in waves of sensation" and that the pain "hits you like a fist, pain so strong you feel it in your guts, your nerve endings."

"I sat alone on election night as the results came in," she writes, "I wanted it that way. I wanted to just let myself be swept up in it."

Gillard also said that Labor lost the election because Kevin Rudd returned without "one truly original new idea" and because he was unable to explain her enduring policy achievements. She believes that the party could muster no reason for his comeback other than that its polling might improve.

"We have some grieving to do together," she says, "But ultimately it has to be grieving for the biggest thing lost, the power to change our nation for the better."

She admits that she was wrong to not contest coalition leader Tony Abbott's labelling of the carbon pricing scheme as a "tax".

"I feared the media would end up playing constant silly word games with me, trying to get me to say the word 'tax'," she says.

"But I made the wrong choice and, politically, it hurt me terribly."

She fiercely defends Labor's policy contributions and appeals to the Labor party to choose future leaders on the basis of substance and purpose rather than opinion polls.

The former prime minister urges her party to learn the lessons from its 1996 loss and make sure it owns its good record in government while also examining which election promises to keep and which to reject.

She says Labor must stand up for its economic record and also policies that are right but may be unpopular, like carbon pricing.

"Labor should not in opposition abandon our carbon pricing scheme," she insists. ? "Climate change is real. Carbon should be priced. Community concern about carbon pricing did abate after its introduction. Tony Abbott does not have a viable alternative."

Abbott, leader of the opposition Coalition, won a crushing victory in national polls last Saturday to end six years of Labor government.