Sheryl Sandberg, the chief operating officer of Facebook, has launched a fierce attack on the gender stereotypes that hold back women at work at the World Economic Forum in Davos.

Sandberg, who is publishing a book called Lean In on women in the workplace in March, singled out T-shirts sold in the US, with the boys' version emblazoned with the words "Smart Like Daddy", while the girls' version says "Pretty like Mommy".

"I would love to say that was 1951, but it was last year," she said. "As a woman becomes more successful, she is less liked, and as a man becomes more successful, he is more liked, and that starts with those T-shirts."

She blasted managers who unconsciously reflect stereotypes when they judge women's performance, saying: "She's great at her job but she's just not as well liked by her peers," or: "She's a bit aggressive."

"They say this with no understanding that this is the penalty women face because of gender stereotypes," she said.

Sandberg also criticised the fact that it is still assumed women will take on the majority of the caring responsibilities at home, even when both parents work. "Women still have two jobs in the most developed countries around the world; men have one."

She added: "From the moment they leave school, the messages for women are different: 'Don't you want to have kids one day?'"

Sandberg was appearing at a panel session in Davos, where five of six speakers were female – the opposite of the gender balance at many Davos events. Only 17% of delegates at the high-powered event are women and in an effort to increase female numbers the organisers now insist that the top 100 "strategic partner" companies that attend and which can bring five delegates must include one women. Many, however, choose to bring only four rather than include a female executive.

The International Monetary Fund managing director, Christine Lagarde, said her experiences of overcoming prejudice had helped her to be a better boss.

"I grew up with brothers; I grew up in a man's world, and you had to elbow your way in.

"I listen more; I'm more attentive to those in the back of the room that sit in the dark and don't want to talk but have a lot to contribute." She said women made better team players: "It's because of our history, it's because of our heritage, it's because of what we've had to face."

Viviene Reding, the European commissioner for justice, fundamental rights and citizenship, had earlier presented data showing that Europe's boardrooms were become more balanced. Last October women made up 15.8% of company boards, up from 13.7% a year ago.

Reding said companies had been forced to become more diverse by the European commission when it declared it would legislate to improve the situation.

"Since the moment that I threatened that if there was no progress then I would put up legislation, there has been real progress," Reding said. "Sometimes it needs a little push."

Reding added that it was crucial for workers to be provided with proper childcare. "This is an issue for men as well as women."

Reding also reminded the WEF that it had not always given gender issues a high profile. "This is the first year that the issue has been presented at a plenary session," she said. "It is a breakthrough for Davos too."

Reding remains committed to bringing in a law that would force companies to favour women over equally qualified men for boardroom positions. "There's not a rigid quota. No one will get a job because she's a woman, but no one will be denied a job because she's a woman."

Elsewhere in Davos, the European Central Bank president, Mario Draghi, told delegates that the optimism surging through the stock exchanges of Europe showed that normality was returning.

"2012 was, to say the least, an interesting year. It was the year of the relaunching of the euro." 2013 must be a year of implementation, he added.

However, Draghi does not expect the economic recovery to begin until the second half of this year.

"Financial markets are enjoying a new sense of relative tranquility," Draghi said, "but it has not fed through to the real economy."

With the eurozone still in recession and unemployment at record levels, Draghi insisted that the pain was "emphatically" worth it, saying the eurozone economy still had many strengths.

"The euro area economy in its entirety has performed better than anywhere in the last 15 years," he said.

Draghi also conceded that European countries had surrendered national sovereignty in the crisis, amid the bailouts and austerity plans. The solution, he added, was to create "supranational sovereignty, where sovereignty is shared".

Jordan's King Abdullah II warned Davos that the Assad regime in Syria would not fall soon, saying they "still have capacity" to hold on to power.

Any fragmentation of the country into small states would be "catastrophic and something that we would be reeling from for decades to come", he added.