Its forces "confirmed the presence of nefarious activity" at the site before getting approval to carry out Sunday's attack, a coalition statement said.
"Early reporting has that seven children at the madrassa died as a result of the strike," it said.
Major Chris Belcher, a coalition spokesman, said: "We are saddened by the innocent lives that were lost as a result of militants' cowardice."
Sgt. 1st Class Dean Welch, another coalition spokesman, said: "If we knew that there were children inside the building, there was no way that that airstrike would have occurred."
The coalition also said it had killed "several dozen" Taliban fighters after their forces were attacked on two occasions in Helmand and Kandahar provinces.
Two foreign soldiers were injured in Sunday's clashes, with coalition forces calling in air strikes in the Kandahar incident.
Street protests
The children's deaths are the latest in a series of civilian deaths involving foreign troops.
More than 120 civilians have been killed by foreign forces in Afghanistan in recent months, according to the Afghan government and residents.
Earlier this month, Hamid Karzai, the president, described the killings as "unacceptable".
The deaths have sparked street protests calling for Karzai's resignation and the withdrawal of US troops from Afghanistan.
The attack, which had the support of Afghan troops, occurred after a bomber blew himself up on a police academy bus in Kabul, killing at least 35 people, in the deadliest suicide attack in Afghanistan since the US-led invasion in 2001.
Al-Qaeda is fighting alongside the Taliban to overthrow Afghanistan's Western-backed government and drive out foreign troops.
Nearly 6,000 people have been killed in Afghanistan over the past 17 months. About 1,500 of them have been civilians.