Mrs Clinton said there would be a joint investigation into the deaths.
The Afghan leader, Hamid Karzai, has said he will raise the incident with Mr Obama but he thanked Mrs Clinton for her statement of regret.
Hillary Clinton: 'There will be a joint investigation'
Pakistan's leader, Asif Ali Zardari, said he would work with Mr Karzai, whom he called his "brother", to defeat the "cancer" of terrorism.
He faces a growing crisis in his own country amid a new outbreak of fighting between the army and Taleban rebels in the Swat Valley region.
In other business, the two South Asian leaders signed a memorandum of understanding on a trade agreement which would boost foreign direct investment in their countries.
But Mrs Clinton acknowledged that such an accord had already been under discussion for more than 40 years without resolution.
Pledge of solidarity
Mrs Clinton said much had been achieved during her talks with Mr Karzai and Mr Zardari.
BBC News, Washington
The Obama administration's attempt to refocus American policy in one of the world's most intractable trouble spots was meant to begin with a diplomatic flourish, the bringing together of the Afghan and Pakistani leaders. It began instead with an American apology for civilian lives lost in Afghanistan.
But while the US grapples with the problems of deploying Mr Obama's reinforcements in Afghanistan, it is events in Pakistan which have been prompting alarm in Washington, where there is concern that the Pakistani seems either unwilling or unable to put down a Taleban insurgency within its own frontiers.
The Obama administration's strategy can only happen if Pakistan, a nuclear-armed traditional military ally of the US, can restore stability and not all Americans are optimistic - one congressman said at the moment Pakistan was a country with its "pants on fire".
"I was extremely impressed by the candour that was really evidenced throughout the meeting, and it was a physical manifestation of our strategy of viewing Afghanistan and Pakistan as a regional challenge, but also a regional opportunity," she said.
Speaking alongside the two leaders, she expressed "personal regret and certainly the sympathy of [the Obama] administration on the loss of civilian life in Afghanistan".
"I want to convey to people of both Afghanistan and Pakistan that we will work very hard with your governments and with your leaders to avoid the loss of innocent life and we deeply, deeply regret that loss," she added.
Thanking her, Mr Karzai said: "We hope we can work together towards reducing, and eventually completely removing, the possibilities of civilian casualties as we move ahead in our war against terrorism."
Mr Zardari said Pakistan would help Afghanistan and the US to fight the threat posed by the Taleban and al-Qaeda.
"For no matter how long it takes and what it takes, democracies will deliver, my democracy will deliver," he said.
"People of Pakistan stand with the people of the United States and the people of Afghanistan."
International Committee of the Red Cross observers who visited the site of the air strikes saw houses destroyed and dozens of dead bodies, including women and children.
The US defence secretary (R) flew into Kabul from Saudi Arabia
Their account was backed up by Afghan officials but they could not confirm the number of casualties.
The US military said coalition troops had been called to assist Afghan forces as they attempted to fight off an insurgent attack. It has sent a team of investigators to Farah.
Meanwhile US Defence Secretary Robert Gates has arrived in Kabul on an unannounced visit.
"We have a new policy, a new strategy, a new ambassador and we have a lot of new troops going into the area, and I just want to go out and see for myself how they're doing," he told reporters in Saudi Arabia shortly before flying to Afghanistan.
Crisis in Pakistan
Mr Obama will hold bilateral talks with Mr Karzai and Mr Zardari, before all three hold a joint meeting.
It's too late now, the incompetent politicians of this blighted land have made the things go beyond the point of no return
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